Triangles — Multiple Choice Questions

Exterior angle of a triangle is equal to:

1. sum of the two opposite adjacent angles

2. sum of the two interior opposite angles

3. adjacent interior angle

4. both 1 and 2

Answer

An exterior angle of a triangle is always equal to the sum of its two opposite interior angles.

Hence, option 2 is the correct option.

In a right angled triangle, the other two angles are always:

1. obtuse angles

2. equal acute angles

3. acute angles

4. Both 2 and 3

Answer

In a right-angled triangle, one angle is 90°, so the other two angles add up to 90°. Therefore each of them must be less than 90°, i.e. acute. They need not be equal.

Hence, option 3 is the correct option.

The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle is:

1. 40°

2. 60°

3. 80°

4. 180°

Answer

Let the angles be 2x, 3x and 4x.

By the angle sum property of a triangle,

⇒ 2x + 3x + 4x = 180°

⇒ 9x = 180°

⇒ x = $\dfrac{180\degree}{9}$

⇒ x = 20°

So the largest angle = 4x = 4 × 20° = 80°.

Hence, option 3 is the correct option.

The angles of a triangle are 50°, 70° and x°. The value of x° is:

1. 60°

2. 120°

3. 100°

4. 50°

Answer

By the angle sum property of a triangle,

⇒ 50° + 70° + x° = 180°

⇒ 120° + x° = 180°

⇒ x° = 180° − 120°

⇒ x° = 60°

Hence, option 1 is the correct option.

The value of x is:

1. 70°

2. 55°

3. 35°

4. 40°

Answer

From the figure,

The two base angles of the triangle are each equal to x and the side BC is produced to D, so 110° is the exterior angle.

By the exterior angle property,

⇒ 110° = x + x

⇒ 110° = 2x

⇒ x = $\dfrac{110\degree}{2}$

⇒ x = 55°

Hence, option 2 is the correct option.

On extending each side of a triangle, on both the sides, the number of exterior angles formed is:

1. 3

2. 6

3. 4

4. 9

Answer

When the sides of a triangle are extended on both the sides, two exterior angles are formed at each of the three vertices, giving 2 × 3 = 6 exterior angles in all.

Hence, option 2 is the correct option.

The value of x is:

1. 30°

2. 45°

3. 60°

4. none of these

Answer

From the figure, the three angles of the triangle are 3x, 60° and x.

By the angle sum property of a triangle,

⇒ 3x + 60° + x = 180°

⇒ 4x + 60° = 180°

⇒ 4x = 180° − 60°

⇒ 4x = 120°

⇒ x = $\dfrac{120\degree}{4}$

⇒ x = 30°

Hence, option 1 is the correct option.

The given triangle is:

1. acute angled triangle

2. right angled triangle

3. obtuse angled triangle

4. isosceles triangle

Answer

From the figure, ∠ABC is an obtuse angle, as it is greater than 90°.

Thus, the given triangle is an obtuse angled triangle.

Hence, option 3 is the correct option.

The measure of angle BAC is:

1. 120°

2. 60°

3. 45°

4. 75°

Answer

From the figure,

In the triangle ABC, AB = BC = CA, thus it is an equilateral triangle.

Each angle of an equilateral triangle = 60°.

Thus, ∠BAC = 60°.

Hence, option 2 is the correct option.

In the given figure, AP is:

1. median

2. bisector of angle BAC

3. bisector of side BC

4. altitude

Answer

From the figure, AP is drawn from the vertex A perpendicular to the opposite side BC, i.e. AP ⊥ BC.

The perpendicular drawn from a vertex of a triangle to the opposite side is called an altitude.

Hence, option 4 is the correct option.