Question

. If the exterior angle of the triangle is 120° and the interior opposite angles are in the ratio 3 : 2, then the measure of the greater angle is

Answer 1

Given :

• Exterior angle of a triangle = 120°
• Ratio of two opposite interior angle = 3 : 2

To find :

• Measure of greater angle

According to the question,

Let,

• The first angle be 3x
• And other angle be 2x

As we know,

• Sum of two interior angle = Exterior angle

➞ 3x + 2x = 120°

➞ 5x = 120°

➞ x = 120° ÷ 5

➞ x = 24°

★ Value of 3x :

➞ 3x

➞ 3(24°)

➞ 72°

★ Value of 2x :

➞ 2x

➞ 2(24°)

➞ 48°

• So, the measure of greater angle is 72°.

___________________________

★ Verification :

We know,

• Sum of two opposite interior angles = Exterior angle

➞ 3x + 2x

➞ 5x

➞ 5(24°)

➞ 120°

∴ L.H.S = R.H.S

Hence, verified.

Answer 2

I hope this is helpful to you...........