Hard
In the figure, ABC is an isosceles triangle (AB=AC) and BD is the bisector of angle B and BD=BC. How much is angle C?
Explanation
Explanation
Let angle B = angle C = beta. Since BD=BC, triangle BDC is isosceles, so angle BDC = angle BCD = beta. In triangle BDC, angle DBC (=beta/2) + angle BCD (beta) + angle BDC (beta) = 180 degrees, giving beta = 72 degrees, which is angle C.
PRO TIP
Re-check your working by substituting the answer back into the original question.