Answer :

A. We have ratio of angles = 5:5:8

Observe that first two angles are equal. So, the triangle is isosceles. Now, we need to check if it is also right-angled.

To find that, let us assume the angles are 5x, 5x and 8x.

We know sum of angles in a triangle is 180°.

⇒ 5x + 5x + 8x = 180°

⇒ 18x = 180°

So, angles are 50°, 50° and 80° that is, it is not a right angled triangle.

Thus, 5:5:8 ⇒ ISOSCELES triangle (option IV)

B. We have ratio of angles = 1:3:5

Let us assume the angles are x, 3x and 5x.

We know sum of angles in a triangle is 180°.

⇒ x + 3x + 5x = 180°

⇒ 9x = 180°

So, angles are 20°, 60° and 100°.

One angle is greater than 90°. So, this triangle has an obtuse angle.

Thus, 1:3:5 ⇒ OBTUSE-ANGLED triangle (option II)

C. We have ratio of angles = 1:1:1

This means all angles in the triangle are equal.

Thus, 1:1:1 ⇒ EQUILATERAL triangle (option V)

D. We have ratio of angles = 1:2:3

Let us assume the angles are x, 2x and 3x.

We know sum of angles in a triangle is 180°.

⇒ x + 2x + 3x = 180°

⇒ 6x = 180°

So, angles are 30°, 60° and 90°.

One angle is equal to 90°. So, this triangle has a right angle.

Thus, 1:2:3 ⇒ RIGHT-ANGLED triangle (option I)

E. We have ratio of angles = 1:1:2

Observe that first two angles are equal. So, the triangle is isosceles. Now, we need to check if it is also right-angled.

To find that, let us assume the angles are x, x and 2x.

We know sum of angles in a triangle is 180°.

⇒ x + x + 2x = 180°

⇒ 4x = 180°

So, angles are 45°, 45° and 90° that is; there is also a right angle in this triangle. This triangle is both right angled and isosceles.

Thus, 1:1:2 ⇒ RIGHT-ANGLED ISOSCELES triangle (option III)

Hence, the answer is A – IV, B – II, C – V, D – I, E – III.

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