Question

Triangle WXY has the interior and exterior angles shown below.

Answer 1

180 - 122 = 58

x + 2x - 13 + 58 = 180
3x + 45 = 180
3x = 135
x = 45

m<W = 2(45) - 13 = 90 - 13 = 77

answer
D. 77

Answer 2

Answer: Fourth option is correct.

Explanation:

Since we have given that

∠ W = (2x-13)°

∠Y = x°

exterior ∠X = 122°

We know that "Sum of interior angles is equal to exterior angles":

`\angle W+\angle Y=122^\circ\\\\2x-13+x=122^\circ\\\\3x-13=122^\circ\\\\3x=122+13\\\\3x=135^\circ\\\\x=(135)/(3)\\\\x=45^\circ`

So, the measure of angle W is given by

`2x-13\\\\=2* 45-13\\\\=90-13\\\\=77^\circ`

Hence, Fourth option is correct.