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THE TRIANGLE AND ITS PROPERTIES

298355 The ratio of the measures of the three angles of a triangle is 2 : 3 : 4. The measure of the largest angle is:

1 80º

2 60º

3 40º

4 180º

Explanation:

80º
Largest angle $= \frac{4}{2 + 3 + 4} \times 180^{\circ} = 80^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298357 In Fig. the value of x is:
3

1 20

2 30

3 40

4 25

Explanation:

30
$∠ TRS + ∠ TRQ = 180^{\circ}$ [Linear angles]
$\Rightarrow 5 x^{\circ} + ∠ TRQ = 180^{\circ}$
$\Rightarrow ∠ TEQ = 180^{\circ} - 5 x^{\circ}$
Now, $∠ QTR + ∠ TRQ = ∠ PQT$ [Exterior angle property of triangle]
$\Rightarrow 3 x^{\circ} + 180^{\circ} - 5 x^{\circ} = 120^{\circ}$
$\Rightarrow 2 x^{\circ} = 60^{\circ}$
$\Rightarrow x = 30$
Hence, the correct answer is option (b).

THE TRIANGLE AND ITS PROPERTIES

298358 In Fig. the value of x is:
4

1 72º

2 50

3 58

4 48

Explanation:

58
$∠ A + ∠ B + ∠ C = 180^{\circ}$ [Angle sum property of triangle]
$\Rightarrow 50^{\circ} + 72^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ C + 122^{\circ} = 180^{\circ}$
$\Rightarrow ∠ C = 58^{\circ}$
Now, $x^{\circ} = ∠ C$ [Vertically opposite angles]
$\Rightarrow x^{\circ} = 58^{\circ}$
$\Rightarrow x = 58$
Hence, the correct answer is option (c).

THE TRIANGLE AND ITS PROPERTIES

298359 In any $△ ABC, AB + BC + CA$ is________________

1

Less than \frac{1}{3} AB

2

Equal to \frac{1}{2} AB

3

Less than AB

4

Greater than 2AB

Explanation:

$Greater than 2AB$
In any Triangle, the sum of any two sides is always greater than the
other side.in $△ ABC, AB + BC > CA . . . . eqn(1)$
$BC + CA > AB . . . . . eqn (2)$
$CA + AB > BC . . . eqn (3)$ In equation (2), adding AB both side we
get, $AB + BC + CA > 2AB$

THE TRIANGLE AND ITS PROPERTIES

298355 The ratio of the measures of the three angles of a triangle is 2 : 3 : 4. The measure of the largest angle is:

1 80º

2 60º

3 40º

4 180º

Explanation:

80º
Largest angle $= \frac{4}{2 + 3 + 4} \times 180^{\circ} = 80^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298357 In Fig. the value of x is:
3

1 20

2 30

3 40

4 25

Explanation:

30
$∠ TRS + ∠ TRQ = 180^{\circ}$ [Linear angles]
$\Rightarrow 5 x^{\circ} + ∠ TRQ = 180^{\circ}$
$\Rightarrow ∠ TEQ = 180^{\circ} - 5 x^{\circ}$
Now, $∠ QTR + ∠ TRQ = ∠ PQT$ [Exterior angle property of triangle]
$\Rightarrow 3 x^{\circ} + 180^{\circ} - 5 x^{\circ} = 120^{\circ}$
$\Rightarrow 2 x^{\circ} = 60^{\circ}$
$\Rightarrow x = 30$
Hence, the correct answer is option (b).

THE TRIANGLE AND ITS PROPERTIES

298358 In Fig. the value of x is:
4

1 72º

2 50

3 58

4 48

Explanation:

58
$∠ A + ∠ B + ∠ C = 180^{\circ}$ [Angle sum property of triangle]
$\Rightarrow 50^{\circ} + 72^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ C + 122^{\circ} = 180^{\circ}$
$\Rightarrow ∠ C = 58^{\circ}$
Now, $x^{\circ} = ∠ C$ [Vertically opposite angles]
$\Rightarrow x^{\circ} = 58^{\circ}$
$\Rightarrow x = 58$
Hence, the correct answer is option (c).

THE TRIANGLE AND ITS PROPERTIES

298359 In any $△ ABC, AB + BC + CA$ is________________

1

Less than \frac{1}{3} AB

2

Equal to \frac{1}{2} AB

3

Less than AB

4

Greater than 2AB

Explanation:

$Greater than 2AB$
In any Triangle, the sum of any two sides is always greater than the
other side.in $△ ABC, AB + BC > CA . . . . eqn(1)$
$BC + CA > AB . . . . . eqn (2)$
$CA + AB > BC . . . eqn (3)$ In equation (2), adding AB both side we
get, $AB + BC + CA > 2AB$

THE TRIANGLE AND ITS PROPERTIES

298355 The ratio of the measures of the three angles of a triangle is 2 : 3 : 4. The measure of the largest angle is:

1 80º

2 60º

3 40º

4 180º

Explanation:

80º
Largest angle $= \frac{4}{2 + 3 + 4} \times 180^{\circ} = 80^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298357 In Fig. the value of x is:
3

1 20

2 30

3 40

4 25

Explanation:

30
$∠ TRS + ∠ TRQ = 180^{\circ}$ [Linear angles]
$\Rightarrow 5 x^{\circ} + ∠ TRQ = 180^{\circ}$
$\Rightarrow ∠ TEQ = 180^{\circ} - 5 x^{\circ}$
Now, $∠ QTR + ∠ TRQ = ∠ PQT$ [Exterior angle property of triangle]
$\Rightarrow 3 x^{\circ} + 180^{\circ} - 5 x^{\circ} = 120^{\circ}$
$\Rightarrow 2 x^{\circ} = 60^{\circ}$
$\Rightarrow x = 30$
Hence, the correct answer is option (b).

THE TRIANGLE AND ITS PROPERTIES

298358 In Fig. the value of x is:
4

1 72º

2 50

3 58

4 48

Explanation:

58
$∠ A + ∠ B + ∠ C = 180^{\circ}$ [Angle sum property of triangle]
$\Rightarrow 50^{\circ} + 72^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ C + 122^{\circ} = 180^{\circ}$
$\Rightarrow ∠ C = 58^{\circ}$
Now, $x^{\circ} = ∠ C$ [Vertically opposite angles]
$\Rightarrow x^{\circ} = 58^{\circ}$
$\Rightarrow x = 58$
Hence, the correct answer is option (c).

THE TRIANGLE AND ITS PROPERTIES

298359 In any $△ ABC, AB + BC + CA$ is________________

1

Less than \frac{1}{3} AB

2

Equal to \frac{1}{2} AB

3

Less than AB

4

Greater than 2AB

Explanation:

$Greater than 2AB$
In any Triangle, the sum of any two sides is always greater than the
other side.in $△ ABC, AB + BC > CA . . . . eqn(1)$
$BC + CA > AB . . . . . eqn (2)$
$CA + AB > BC . . . eqn (3)$ In equation (2), adding AB both side we
get, $AB + BC + CA > 2AB$

THE TRIANGLE AND ITS PROPERTIES

298355 The ratio of the measures of the three angles of a triangle is 2 : 3 : 4. The measure of the largest angle is:

1 80º

2 60º

3 40º

4 180º

Explanation:

80º
Largest angle $= \frac{4}{2 + 3 + 4} \times 180^{\circ} = 80^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298357 In Fig. the value of x is:
3

1 20

2 30

3 40

4 25

Explanation:

30
$∠ TRS + ∠ TRQ = 180^{\circ}$ [Linear angles]
$\Rightarrow 5 x^{\circ} + ∠ TRQ = 180^{\circ}$
$\Rightarrow ∠ TEQ = 180^{\circ} - 5 x^{\circ}$
Now, $∠ QTR + ∠ TRQ = ∠ PQT$ [Exterior angle property of triangle]
$\Rightarrow 3 x^{\circ} + 180^{\circ} - 5 x^{\circ} = 120^{\circ}$
$\Rightarrow 2 x^{\circ} = 60^{\circ}$
$\Rightarrow x = 30$
Hence, the correct answer is option (b).

THE TRIANGLE AND ITS PROPERTIES

298358 In Fig. the value of x is:
4

1 72º

2 50

3 58

4 48

Explanation:

58
$∠ A + ∠ B + ∠ C = 180^{\circ}$ [Angle sum property of triangle]
$\Rightarrow 50^{\circ} + 72^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ C + 122^{\circ} = 180^{\circ}$
$\Rightarrow ∠ C = 58^{\circ}$
Now, $x^{\circ} = ∠ C$ [Vertically opposite angles]
$\Rightarrow x^{\circ} = 58^{\circ}$
$\Rightarrow x = 58$
Hence, the correct answer is option (c).

THE TRIANGLE AND ITS PROPERTIES

298359 In any $△ ABC, AB + BC + CA$ is________________

1

Less than \frac{1}{3} AB

2

Equal to \frac{1}{2} AB

3

Less than AB

4

Greater than 2AB

Explanation:

$Greater than 2AB$
In any Triangle, the sum of any two sides is always greater than the
other side.in $△ ABC, AB + BC > CA . . . . eqn(1)$
$BC + CA > AB . . . . . eqn (2)$
$CA + AB > BC . . . eqn (3)$ In equation (2), adding AB both side we
get, $AB + BC + CA > 2AB$

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