Question

one side of a triangle is produced and the exterior angle is produced and the exterior angle so fromed is 120° if the interior opposite angles be in the ratio 3:5, find the measure of each angle of the triangle​

Answer 1

Answer :

• 45⁰ and 75⁰ are the measure of each angle of the triangle

Given :

• One side of a triangle is produced and the exterior angle is produced and the exterior anglenis formed is 120⁰
• If the interior angle opposite angles be in the ratio 3 : 5

To find :

• Measure of each angle of the triangle

Solution :

• Let the angle be x

We know that

• Exterior angle = Sum of opposite angle

Given ,

• The ratio is 3:5 so,

• Let the first ratio be 3x
• Let the second ratio be 5x

• Exterior angle is 120⁰

↦ 3x + 5x = 120

↦ 8x = 120

↦x = 120/8

↦ x = 15

Finding the measure of each angle of the triangle :

↦ 3x

↦ 3(15)

↦ 45⁰

↦ 5x

↦ 5(15)

↦ 75

Hence , 45⁰ and 75⁰ are the measure of each angle of the triangle

Verification :

↦ 3x + 5x = 120⁰

↦ 3(15) + 5(15) = 120⁰

↦ 45 + 75 = 120⁰

↦ 120⁰ = 120⁰

Hence , Verified