Question

Your Turn: Find the measure of angle P below. Show your work. *

Answer 1

2x+5+(7x-14)=180

9x-9=180

9x=189

x=21

2x+5=P

2(21)+5= 47

P=47

Answer 2

Check the picture.

The figure shows lines m, n and the line through points A And B, call it $l_{AB}$.

1. The angles ABC and CBP  are  "supplementary" angles, that is angles whose sum is 180°, because together they form one straight angle.

thus, 

(2x+5°)+(7x-14°)=180°

9x-9°=180°

9x=189°

x=189°/9=21°.


2. Remark, m and n are parallel, otherwise we can say nothing about the measure of angle P

check the second picture, notice the F shape formed by CBP and P.

Angles CBP and P are called "angles F" or "corresponding angles".

Corresponding angles formed by a line cutting 2 parallel lines, are always congruent (that is equal) so:

m(P)=m(CBP)=7x-14°=7.21°-14°=147°-14°=133°


Answer: 133°