Question

Find the measure of exterior angle tuv below .​

Answer 1

Given:

m∠T = 61°

m∠S = 5x - 15

m ext∠TUV = 8x - 8

To find:

The measure of exterior angle TUV

Solution:

STU is a triangle.

By exterior angle of triangle property:

The measure of an exterior angle is equal to the sum of the opposite interior angles.

m ext∠TUV = m∠T + m∠S

8x - 8 = 61 + 5x - 15

8x - 8 = 46 + 5x

Add 8 on both sides.

8x - 8 + 8 = 46 + 5x + 8

8x = 54 + 5x

Subtract 5x from both sides.

8x - 5x = 54 + 5x - 5x

3x = 54

Divide by 3 on both sides.

`$(3x)/(3) =(54)/(3)`

x = 18

Substitute x = 18 in m ext∠TUV.

m ext∠TUV = 8(18) - 8

= 144 - 8

= 136

Therefore measure of exterior angle ∠TUV is 136°.