Check the picture.
The figure shows lines m, n and the line through points A And B, call it [tex]l_{AB}[/tex].
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°
