Problem: Triangle ABC is isosceles with base AC. Points P and Q are respectively in CB and AB and such that AC=AP=PQ=QB. The number of degrees in angle B is:
Answer Choices:
A. 2575
B. 2631
C. 30
D. 40
E. Not determined by the information given.
Solution:
Represent the magnitude of angle B by m. Then, In order, we obtain angle QPB =m, angle AQP=2 m, angle QAP=2 m, angle QPA =180−4 m, angle APC=3 m, angle ACP=3 m, and angle PAC=180−6 m. Since angle BAC= angle BCA,180−6m+2m =3 \mathrm{~m} \quad \therefore \mathrm{~m}=25 \frac{5}