Question

Refer to the figure at the right. What is m∠P?

Figure P Q R S T is a 5 sided figure. Angle measures are as follows: Q equals 6 x minus 6 degrees. R equals 4 x minus 10 degrees. S equals 5 x minus 11 degrees. T equals 5 x plus 13 degrees. P equals 4 x plus 2 degrees.

Answer 1

Sum the interior angles of a pentagon: (5−2)·180 = 540°. So
(6x−6)+(4x−10)+(5x−11)+(5x+13)+(4x+2)=540.

Combine terms: 24x − 12 = 540 → 24x = 552 → x = 23.

Then m∠P = 4x + 2 = 4(23) + 2 = 94°.
Answer: 94°.