NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
THE TRIANGLE AND ITS PROPERTIES
298453
In Fig. if AB || CD, then the values of x and y are: 1
1 x = 106, y = 307
2 x = 307, y = 106
3 x =107, y = 306
4 x = 105, y = 308
Explanation:
x = 106, y = 307 In \(\triangle \text{CDE}\) \(\angle \text{CDE}+\angle \text{CED}+\angle \text{ECD}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 53^\circ+53^\circ+\angle \text{ECD}=180^\circ\) \(\Rightarrow \angle \text{ECD}=74^\circ\) Since, AB || CD \(\therefore \angle \text{ECD}=\angle \text{CGB}=74^\circ\) [Corresponding angles] Now, \(\angle \text{CGB}+\angle \text{BGF}=180^\circ\) [Linear pair angles] \(\Rightarrow 74^\circ+\text{x}^\circ=180^\circ\) \(\Rightarrow \text{x}=106\) Now, In \(\triangle \text{EGB},\) \(\angle \text{EGB}+\angle \text{BEG}+\angle \text{EBG}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 74^\circ+53^\circ+\angle \text{EBG}=180^\circ\) \(\Rightarrow \angle \text{EBG}=53^\circ\) Now, \(\angle \text{EBG}+\text{Reflex }\angle \text{EBG}=360^\circ\) [Complete angle] \(\Rightarrow 53^\circ+\text{y}^\circ=360^\circ\) \(\Rightarrow \text{y}=307\) Hence, the correct answer is option (a).
THE TRIANGLE AND ITS PROPERTIES
298454
If one angle of a triangle is obtuse, the triangle is called:
1 Acute-angled
2 Obtuse-angled
3 Right-angled
4 None of these
Explanation:
Obtuse-angled
THE TRIANGLE AND ITS PROPERTIES
298455
In \(\triangle\text{ABC},\) \(\angle\text{A}=50^{\circ},\)\(\angle\text{B}=70^{\circ}\) and bisector of \(\angle\text{C}\) Meets AB in D figure. Measure of \(\angle\text{ADC}\) is. 2
1 50°
2 100°
3 30°
4 70°
Explanation:
100° In \(\triangle\text{ADC},\) \(\angle\text{ADC}+\angle\text{DAC}+\angle\text{ACD}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{ADC}+50^{\circ}+\angle\text{ACD}=180^{\circ}\) \([\because\angle\text{DAC}=50^{0}]\) \(\Rightarrow \ \angle\text{ACD}=130^{\circ}-\angle\text{ACD}......(\text{i})\) In \(\triangle\text{ DBC},\) \(\angle\text{ADC}=\angle\text{DBC}+\angle\text{BCD}\) \([\because\) exterior angle is equal to sum of opposite interior angles\(]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+\angle\text{ACD}\) \([\because\angle\text{ACD}=\angle\text{BCD}]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+130^{\circ}-\angle\text{ADC}\) [from equation (i)] \(\Rightarrow \ \angle\text{ADC}=200^{\circ}-\angle\text{ADC}\) \(\Rightarrow 2\ \angle\text{ADC}=200^{\circ}\) \(\Rightarrow \ \angle\text{ADC}=\frac{200^{\circ}}{2}\) \(\Rightarrow \ \angle\text{ADC}=100^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298472
Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the:
1 RHS congruence criterion.
2 ASA congruence criterion.
3 SAS congruence criterion.
4 AAA congruence criterion.
Explanation:
ASA congruence criterion. Under ASA congruence criterion, two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle.
298453
In Fig. if AB || CD, then the values of x and y are: 1
1 x = 106, y = 307
2 x = 307, y = 106
3 x =107, y = 306
4 x = 105, y = 308
Explanation:
x = 106, y = 307 In \(\triangle \text{CDE}\) \(\angle \text{CDE}+\angle \text{CED}+\angle \text{ECD}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 53^\circ+53^\circ+\angle \text{ECD}=180^\circ\) \(\Rightarrow \angle \text{ECD}=74^\circ\) Since, AB || CD \(\therefore \angle \text{ECD}=\angle \text{CGB}=74^\circ\) [Corresponding angles] Now, \(\angle \text{CGB}+\angle \text{BGF}=180^\circ\) [Linear pair angles] \(\Rightarrow 74^\circ+\text{x}^\circ=180^\circ\) \(\Rightarrow \text{x}=106\) Now, In \(\triangle \text{EGB},\) \(\angle \text{EGB}+\angle \text{BEG}+\angle \text{EBG}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 74^\circ+53^\circ+\angle \text{EBG}=180^\circ\) \(\Rightarrow \angle \text{EBG}=53^\circ\) Now, \(\angle \text{EBG}+\text{Reflex }\angle \text{EBG}=360^\circ\) [Complete angle] \(\Rightarrow 53^\circ+\text{y}^\circ=360^\circ\) \(\Rightarrow \text{y}=307\) Hence, the correct answer is option (a).
THE TRIANGLE AND ITS PROPERTIES
298454
If one angle of a triangle is obtuse, the triangle is called:
1 Acute-angled
2 Obtuse-angled
3 Right-angled
4 None of these
Explanation:
Obtuse-angled
THE TRIANGLE AND ITS PROPERTIES
298455
In \(\triangle\text{ABC},\) \(\angle\text{A}=50^{\circ},\)\(\angle\text{B}=70^{\circ}\) and bisector of \(\angle\text{C}\) Meets AB in D figure. Measure of \(\angle\text{ADC}\) is. 2
1 50°
2 100°
3 30°
4 70°
Explanation:
100° In \(\triangle\text{ADC},\) \(\angle\text{ADC}+\angle\text{DAC}+\angle\text{ACD}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{ADC}+50^{\circ}+\angle\text{ACD}=180^{\circ}\) \([\because\angle\text{DAC}=50^{0}]\) \(\Rightarrow \ \angle\text{ACD}=130^{\circ}-\angle\text{ACD}......(\text{i})\) In \(\triangle\text{ DBC},\) \(\angle\text{ADC}=\angle\text{DBC}+\angle\text{BCD}\) \([\because\) exterior angle is equal to sum of opposite interior angles\(]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+\angle\text{ACD}\) \([\because\angle\text{ACD}=\angle\text{BCD}]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+130^{\circ}-\angle\text{ADC}\) [from equation (i)] \(\Rightarrow \ \angle\text{ADC}=200^{\circ}-\angle\text{ADC}\) \(\Rightarrow 2\ \angle\text{ADC}=200^{\circ}\) \(\Rightarrow \ \angle\text{ADC}=\frac{200^{\circ}}{2}\) \(\Rightarrow \ \angle\text{ADC}=100^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298472
Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the:
1 RHS congruence criterion.
2 ASA congruence criterion.
3 SAS congruence criterion.
4 AAA congruence criterion.
Explanation:
ASA congruence criterion. Under ASA congruence criterion, two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle.
298453
In Fig. if AB || CD, then the values of x and y are: 1
1 x = 106, y = 307
2 x = 307, y = 106
3 x =107, y = 306
4 x = 105, y = 308
Explanation:
x = 106, y = 307 In \(\triangle \text{CDE}\) \(\angle \text{CDE}+\angle \text{CED}+\angle \text{ECD}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 53^\circ+53^\circ+\angle \text{ECD}=180^\circ\) \(\Rightarrow \angle \text{ECD}=74^\circ\) Since, AB || CD \(\therefore \angle \text{ECD}=\angle \text{CGB}=74^\circ\) [Corresponding angles] Now, \(\angle \text{CGB}+\angle \text{BGF}=180^\circ\) [Linear pair angles] \(\Rightarrow 74^\circ+\text{x}^\circ=180^\circ\) \(\Rightarrow \text{x}=106\) Now, In \(\triangle \text{EGB},\) \(\angle \text{EGB}+\angle \text{BEG}+\angle \text{EBG}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 74^\circ+53^\circ+\angle \text{EBG}=180^\circ\) \(\Rightarrow \angle \text{EBG}=53^\circ\) Now, \(\angle \text{EBG}+\text{Reflex }\angle \text{EBG}=360^\circ\) [Complete angle] \(\Rightarrow 53^\circ+\text{y}^\circ=360^\circ\) \(\Rightarrow \text{y}=307\) Hence, the correct answer is option (a).
THE TRIANGLE AND ITS PROPERTIES
298454
If one angle of a triangle is obtuse, the triangle is called:
1 Acute-angled
2 Obtuse-angled
3 Right-angled
4 None of these
Explanation:
Obtuse-angled
THE TRIANGLE AND ITS PROPERTIES
298455
In \(\triangle\text{ABC},\) \(\angle\text{A}=50^{\circ},\)\(\angle\text{B}=70^{\circ}\) and bisector of \(\angle\text{C}\) Meets AB in D figure. Measure of \(\angle\text{ADC}\) is. 2
1 50°
2 100°
3 30°
4 70°
Explanation:
100° In \(\triangle\text{ADC},\) \(\angle\text{ADC}+\angle\text{DAC}+\angle\text{ACD}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{ADC}+50^{\circ}+\angle\text{ACD}=180^{\circ}\) \([\because\angle\text{DAC}=50^{0}]\) \(\Rightarrow \ \angle\text{ACD}=130^{\circ}-\angle\text{ACD}......(\text{i})\) In \(\triangle\text{ DBC},\) \(\angle\text{ADC}=\angle\text{DBC}+\angle\text{BCD}\) \([\because\) exterior angle is equal to sum of opposite interior angles\(]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+\angle\text{ACD}\) \([\because\angle\text{ACD}=\angle\text{BCD}]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+130^{\circ}-\angle\text{ADC}\) [from equation (i)] \(\Rightarrow \ \angle\text{ADC}=200^{\circ}-\angle\text{ADC}\) \(\Rightarrow 2\ \angle\text{ADC}=200^{\circ}\) \(\Rightarrow \ \angle\text{ADC}=\frac{200^{\circ}}{2}\) \(\Rightarrow \ \angle\text{ADC}=100^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298472
Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the:
1 RHS congruence criterion.
2 ASA congruence criterion.
3 SAS congruence criterion.
4 AAA congruence criterion.
Explanation:
ASA congruence criterion. Under ASA congruence criterion, two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle.
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
THE TRIANGLE AND ITS PROPERTIES
298453
In Fig. if AB || CD, then the values of x and y are: 1
1 x = 106, y = 307
2 x = 307, y = 106
3 x =107, y = 306
4 x = 105, y = 308
Explanation:
x = 106, y = 307 In \(\triangle \text{CDE}\) \(\angle \text{CDE}+\angle \text{CED}+\angle \text{ECD}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 53^\circ+53^\circ+\angle \text{ECD}=180^\circ\) \(\Rightarrow \angle \text{ECD}=74^\circ\) Since, AB || CD \(\therefore \angle \text{ECD}=\angle \text{CGB}=74^\circ\) [Corresponding angles] Now, \(\angle \text{CGB}+\angle \text{BGF}=180^\circ\) [Linear pair angles] \(\Rightarrow 74^\circ+\text{x}^\circ=180^\circ\) \(\Rightarrow \text{x}=106\) Now, In \(\triangle \text{EGB},\) \(\angle \text{EGB}+\angle \text{BEG}+\angle \text{EBG}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow 74^\circ+53^\circ+\angle \text{EBG}=180^\circ\) \(\Rightarrow \angle \text{EBG}=53^\circ\) Now, \(\angle \text{EBG}+\text{Reflex }\angle \text{EBG}=360^\circ\) [Complete angle] \(\Rightarrow 53^\circ+\text{y}^\circ=360^\circ\) \(\Rightarrow \text{y}=307\) Hence, the correct answer is option (a).
THE TRIANGLE AND ITS PROPERTIES
298454
If one angle of a triangle is obtuse, the triangle is called:
1 Acute-angled
2 Obtuse-angled
3 Right-angled
4 None of these
Explanation:
Obtuse-angled
THE TRIANGLE AND ITS PROPERTIES
298455
In \(\triangle\text{ABC},\) \(\angle\text{A}=50^{\circ},\)\(\angle\text{B}=70^{\circ}\) and bisector of \(\angle\text{C}\) Meets AB in D figure. Measure of \(\angle\text{ADC}\) is. 2
1 50°
2 100°
3 30°
4 70°
Explanation:
100° In \(\triangle\text{ADC},\) \(\angle\text{ADC}+\angle\text{DAC}+\angle\text{ACD}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{ADC}+50^{\circ}+\angle\text{ACD}=180^{\circ}\) \([\because\angle\text{DAC}=50^{0}]\) \(\Rightarrow \ \angle\text{ACD}=130^{\circ}-\angle\text{ACD}......(\text{i})\) In \(\triangle\text{ DBC},\) \(\angle\text{ADC}=\angle\text{DBC}+\angle\text{BCD}\) \([\because\) exterior angle is equal to sum of opposite interior angles\(]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+\angle\text{ACD}\) \([\because\angle\text{ACD}=\angle\text{BCD}]\) \(\Rightarrow \ \angle\text{ADC}=70^{\circ}+130^{\circ}-\angle\text{ADC}\) [from equation (i)] \(\Rightarrow \ \angle\text{ADC}=200^{\circ}-\angle\text{ADC}\) \(\Rightarrow 2\ \angle\text{ADC}=200^{\circ}\) \(\Rightarrow \ \angle\text{ADC}=\frac{200^{\circ}}{2}\) \(\Rightarrow \ \angle\text{ADC}=100^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298472
Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the:
1 RHS congruence criterion.
2 ASA congruence criterion.
3 SAS congruence criterion.
4 AAA congruence criterion.
Explanation:
ASA congruence criterion. Under ASA congruence criterion, two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle.
1