Question

M∠qps=40°, m∠rps = (8x + 7)°, and m∠qpr = (9x + 16)°. find the measure of x. show your work.

Answer 1

The sum of angles in a triangle is 180°

40°+(8x+7)°+(9x+16)° = 180°
40 + 8x + 7 + 9x + 16 = 180°
40 + 7 + 16 + 8x + 9x = 180°
63 + 17x = 180°
17x = 180 - 63
17x = 117
x = 117 ÷ 17
x = 6.9 °

Answer 2

The answer is actually 1. I tried it and I got it correct. This is what you have to do:

<QPR+<RPS=<QPS

(9x+16) + (8x+7)=40

17x+23=40

17x=17

x=1