Question

Find the measure of exterior angle TUV below . please show step by step insturctions.

Answer 1

Explanation:

<TUV = 8x -8°

<STU = 67°

<TSU = 5x - 15°

Now

<TUV = <STU + <TSU <exterior angle of a triangle is equal to the sum of two opposite interior angle >

8x - 8° = 67° + 5x -15°

8x - 5x = 67° - 15° + 8°

3x = 60°

Therefore x = 20°

<TUV = 8 *20° - 8° = 160°-8° = 152°

Answer 2

Answer: TUV = 36 degrees

Explanation:

The sum of the angles in a straight line is 180 degrees. It means that

Angle TUS + angle TUV = 180

TUS + 8x - 8 = 180

TUS = 180 + 8 - 8x

TUS = 188 - 8x

Also, the sum of the angles in a triangle is 180 degrees. It means that

61 + 5x - 15 + TUS = 180

TUS = 180 + 15 - 61 - 5x

TUS = 134 - 5x

Therefore,

188 - 8x = 134 - 5x

- 5x + 8x = 188 - 134

3x = 54

x = 54/3

x = 18

Therefore,

TUV = 8x - 8 = (8 × 18) - 8 = 136 degrees