298379
From the following figure, the value of x is: 4
1 75°
2 90°
3 120°
4 60°
Explanation:
120° \(\text{In} \ \triangle\text{ABC},\) \(\angle\text{CAB}+\angle\text{ABC}+\angle\text{BCA}=180^{\circ}\) \([\text{angle sum property of a triangle}]\) \(\Rightarrow \ 25^{\circ}+35^{\circ}+\angle\text{BCA}=180^{\circ}\) \(\Rightarrow\angle\text{BCA}=180^{\circ}-60^{\circ}\) \(\Rightarrow \ \angle\text{BCA}=120^{\circ}\) Also, \(\ \angle\text{BCA}\) is an exterior angle. \(\therefore \ \angle\text{BCA}=\angle\text{D}+\text{y}\) \(\Rightarrow \ \text{y}=\angle\text{BCA}-\angle\text{D}=120^{\circ}-60^{\circ}\) \(\Rightarrow \ \text{y}=60^{\circ}\) Now, \(\angle\text{x}\) and \(\angle\text{y}\) form a linear pair. \(\therefore \ \text{x}+\text{y}=180^{\circ}\) \(\Rightarrow \ \text{x}+\text{60}^{\circ}=180^{\circ}\) \(\Rightarrow \ \text{x}=180^{\circ}-60^{\circ}=120^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298380
Two trees 7m and 4m high stand upright on a ground. If their bases (roots) are 4m apart, then the distance between their tops is:
1 3m
2 5m
3 4m
4 1m
Explanation:
5m Let BE be the smaller tree and AD be the bigger tree. Now, we have to find AB (i.e. the distance between their tops). 5 By observing, ED = BC = 4m and BE = CD = 4m \(\text{In} \ \triangle\text{ABC},\) BC = 4m and AC = AD - CD = (7 - 4)m = 3m In right angled \( \ \triangle\text{ABC},\) AB = AC\(^{1}\) + BC\(^{1}\) = 4\(^{1}\) + 3\(^{1}\) [by pythagoras theoram] = 16 + 9 AB\(^{1}\) = 25 \(? \text{AB} = \sqrt{25}\) \(\Rightarrow \ \text{AB}=5\text{m}\) Therefore, distance between thier tops is 5m.
THE TRIANGLE AND ITS PROPERTIES
298381
If one angle of a triangle is equal to the sum of the other two angles, the triangle is:
1 obtuse.
2 acute.
3 right.
4 equilateral.
Explanation:
right. Let A, B and C be the angles of the triangle. Then, one angle of a triangle is equal to the sum of the other two angles. i.e. \(\angle\text{A}+\angle\text{B}+\angle\text{C}.....(\text{i})\) As we know, \(\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{A}+\angle\text{A}=180^{\circ}\) \(\Rightarrow \ 2\angle\text{A}=180^{\circ}\) \(\angle\text{A}=\frac{180^{\circ}}{2}\) \(\Rightarrow \ \angle=90^{\circ}\) Hence, the triangle is right angled.
THE TRIANGLE AND ITS PROPERTIES
298382
In \(\triangle\text{PQR},\) PM is. 6
1 Median
2 Side
3 Bisector
4 Altitude
Explanation:
Altitude If the line from the vertex to the opposite side makes 90 - degree angle( or perpendicular ) with the side, then it is altitude.
298379
From the following figure, the value of x is: 4
1 75°
2 90°
3 120°
4 60°
Explanation:
120° \(\text{In} \ \triangle\text{ABC},\) \(\angle\text{CAB}+\angle\text{ABC}+\angle\text{BCA}=180^{\circ}\) \([\text{angle sum property of a triangle}]\) \(\Rightarrow \ 25^{\circ}+35^{\circ}+\angle\text{BCA}=180^{\circ}\) \(\Rightarrow\angle\text{BCA}=180^{\circ}-60^{\circ}\) \(\Rightarrow \ \angle\text{BCA}=120^{\circ}\) Also, \(\ \angle\text{BCA}\) is an exterior angle. \(\therefore \ \angle\text{BCA}=\angle\text{D}+\text{y}\) \(\Rightarrow \ \text{y}=\angle\text{BCA}-\angle\text{D}=120^{\circ}-60^{\circ}\) \(\Rightarrow \ \text{y}=60^{\circ}\) Now, \(\angle\text{x}\) and \(\angle\text{y}\) form a linear pair. \(\therefore \ \text{x}+\text{y}=180^{\circ}\) \(\Rightarrow \ \text{x}+\text{60}^{\circ}=180^{\circ}\) \(\Rightarrow \ \text{x}=180^{\circ}-60^{\circ}=120^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298380
Two trees 7m and 4m high stand upright on a ground. If their bases (roots) are 4m apart, then the distance between their tops is:
1 3m
2 5m
3 4m
4 1m
Explanation:
5m Let BE be the smaller tree and AD be the bigger tree. Now, we have to find AB (i.e. the distance between their tops). 5 By observing, ED = BC = 4m and BE = CD = 4m \(\text{In} \ \triangle\text{ABC},\) BC = 4m and AC = AD - CD = (7 - 4)m = 3m In right angled \( \ \triangle\text{ABC},\) AB = AC\(^{1}\) + BC\(^{1}\) = 4\(^{1}\) + 3\(^{1}\) [by pythagoras theoram] = 16 + 9 AB\(^{1}\) = 25 \(? \text{AB} = \sqrt{25}\) \(\Rightarrow \ \text{AB}=5\text{m}\) Therefore, distance between thier tops is 5m.
THE TRIANGLE AND ITS PROPERTIES
298381
If one angle of a triangle is equal to the sum of the other two angles, the triangle is:
1 obtuse.
2 acute.
3 right.
4 equilateral.
Explanation:
right. Let A, B and C be the angles of the triangle. Then, one angle of a triangle is equal to the sum of the other two angles. i.e. \(\angle\text{A}+\angle\text{B}+\angle\text{C}.....(\text{i})\) As we know, \(\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{A}+\angle\text{A}=180^{\circ}\) \(\Rightarrow \ 2\angle\text{A}=180^{\circ}\) \(\angle\text{A}=\frac{180^{\circ}}{2}\) \(\Rightarrow \ \angle=90^{\circ}\) Hence, the triangle is right angled.
THE TRIANGLE AND ITS PROPERTIES
298382
In \(\triangle\text{PQR},\) PM is. 6
1 Median
2 Side
3 Bisector
4 Altitude
Explanation:
Altitude If the line from the vertex to the opposite side makes 90 - degree angle( or perpendicular ) with the side, then it is altitude.
298379
From the following figure, the value of x is: 4
1 75°
2 90°
3 120°
4 60°
Explanation:
120° \(\text{In} \ \triangle\text{ABC},\) \(\angle\text{CAB}+\angle\text{ABC}+\angle\text{BCA}=180^{\circ}\) \([\text{angle sum property of a triangle}]\) \(\Rightarrow \ 25^{\circ}+35^{\circ}+\angle\text{BCA}=180^{\circ}\) \(\Rightarrow\angle\text{BCA}=180^{\circ}-60^{\circ}\) \(\Rightarrow \ \angle\text{BCA}=120^{\circ}\) Also, \(\ \angle\text{BCA}\) is an exterior angle. \(\therefore \ \angle\text{BCA}=\angle\text{D}+\text{y}\) \(\Rightarrow \ \text{y}=\angle\text{BCA}-\angle\text{D}=120^{\circ}-60^{\circ}\) \(\Rightarrow \ \text{y}=60^{\circ}\) Now, \(\angle\text{x}\) and \(\angle\text{y}\) form a linear pair. \(\therefore \ \text{x}+\text{y}=180^{\circ}\) \(\Rightarrow \ \text{x}+\text{60}^{\circ}=180^{\circ}\) \(\Rightarrow \ \text{x}=180^{\circ}-60^{\circ}=120^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298380
Two trees 7m and 4m high stand upright on a ground. If their bases (roots) are 4m apart, then the distance between their tops is:
1 3m
2 5m
3 4m
4 1m
Explanation:
5m Let BE be the smaller tree and AD be the bigger tree. Now, we have to find AB (i.e. the distance between their tops). 5 By observing, ED = BC = 4m and BE = CD = 4m \(\text{In} \ \triangle\text{ABC},\) BC = 4m and AC = AD - CD = (7 - 4)m = 3m In right angled \( \ \triangle\text{ABC},\) AB = AC\(^{1}\) + BC\(^{1}\) = 4\(^{1}\) + 3\(^{1}\) [by pythagoras theoram] = 16 + 9 AB\(^{1}\) = 25 \(? \text{AB} = \sqrt{25}\) \(\Rightarrow \ \text{AB}=5\text{m}\) Therefore, distance between thier tops is 5m.
THE TRIANGLE AND ITS PROPERTIES
298381
If one angle of a triangle is equal to the sum of the other two angles, the triangle is:
1 obtuse.
2 acute.
3 right.
4 equilateral.
Explanation:
right. Let A, B and C be the angles of the triangle. Then, one angle of a triangle is equal to the sum of the other two angles. i.e. \(\angle\text{A}+\angle\text{B}+\angle\text{C}.....(\text{i})\) As we know, \(\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{A}+\angle\text{A}=180^{\circ}\) \(\Rightarrow \ 2\angle\text{A}=180^{\circ}\) \(\angle\text{A}=\frac{180^{\circ}}{2}\) \(\Rightarrow \ \angle=90^{\circ}\) Hence, the triangle is right angled.
THE TRIANGLE AND ITS PROPERTIES
298382
In \(\triangle\text{PQR},\) PM is. 6
1 Median
2 Side
3 Bisector
4 Altitude
Explanation:
Altitude If the line from the vertex to the opposite side makes 90 - degree angle( or perpendicular ) with the side, then it is altitude.
298379
From the following figure, the value of x is: 4
1 75°
2 90°
3 120°
4 60°
Explanation:
120° \(\text{In} \ \triangle\text{ABC},\) \(\angle\text{CAB}+\angle\text{ABC}+\angle\text{BCA}=180^{\circ}\) \([\text{angle sum property of a triangle}]\) \(\Rightarrow \ 25^{\circ}+35^{\circ}+\angle\text{BCA}=180^{\circ}\) \(\Rightarrow\angle\text{BCA}=180^{\circ}-60^{\circ}\) \(\Rightarrow \ \angle\text{BCA}=120^{\circ}\) Also, \(\ \angle\text{BCA}\) is an exterior angle. \(\therefore \ \angle\text{BCA}=\angle\text{D}+\text{y}\) \(\Rightarrow \ \text{y}=\angle\text{BCA}-\angle\text{D}=120^{\circ}-60^{\circ}\) \(\Rightarrow \ \text{y}=60^{\circ}\) Now, \(\angle\text{x}\) and \(\angle\text{y}\) form a linear pair. \(\therefore \ \text{x}+\text{y}=180^{\circ}\) \(\Rightarrow \ \text{x}+\text{60}^{\circ}=180^{\circ}\) \(\Rightarrow \ \text{x}=180^{\circ}-60^{\circ}=120^{\circ}\)
THE TRIANGLE AND ITS PROPERTIES
298380
Two trees 7m and 4m high stand upright on a ground. If their bases (roots) are 4m apart, then the distance between their tops is:
1 3m
2 5m
3 4m
4 1m
Explanation:
5m Let BE be the smaller tree and AD be the bigger tree. Now, we have to find AB (i.e. the distance between their tops). 5 By observing, ED = BC = 4m and BE = CD = 4m \(\text{In} \ \triangle\text{ABC},\) BC = 4m and AC = AD - CD = (7 - 4)m = 3m In right angled \( \ \triangle\text{ABC},\) AB = AC\(^{1}\) + BC\(^{1}\) = 4\(^{1}\) + 3\(^{1}\) [by pythagoras theoram] = 16 + 9 AB\(^{1}\) = 25 \(? \text{AB} = \sqrt{25}\) \(\Rightarrow \ \text{AB}=5\text{m}\) Therefore, distance between thier tops is 5m.
THE TRIANGLE AND ITS PROPERTIES
298381
If one angle of a triangle is equal to the sum of the other two angles, the triangle is:
1 obtuse.
2 acute.
3 right.
4 equilateral.
Explanation:
right. Let A, B and C be the angles of the triangle. Then, one angle of a triangle is equal to the sum of the other two angles. i.e. \(\angle\text{A}+\angle\text{B}+\angle\text{C}.....(\text{i})\) As we know, \(\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}\) [angle sum property of a triangle] \(\Rightarrow \ \angle\text{A}+\angle\text{A}=180^{\circ}\) \(\Rightarrow \ 2\angle\text{A}=180^{\circ}\) \(\angle\text{A}=\frac{180^{\circ}}{2}\) \(\Rightarrow \ \angle=90^{\circ}\) Hence, the triangle is right angled.
THE TRIANGLE AND ITS PROPERTIES
298382
In \(\triangle\text{PQR},\) PM is. 6
1 Median
2 Side
3 Bisector
4 Altitude
Explanation:
Altitude If the line from the vertex to the opposite side makes 90 - degree angle( or perpendicular ) with the side, then it is altitude.
4
