Question

If m∠BAD = 65, what is the m∠DCB? (picture included)

Answer 1

ABD is isosceles triangle

so ∡BAD = ∡ BDA = 65

∡BDA + ∡BDC = 180 (supplementary angles)

so ∡BDC = 180-65 = 115

BCD is also isosceles triangle

∡DCB=∡DBC

and ∡DCB+∡DBC+BDC =180

2∡DCB = 180-115 = 65

thus ∡DCB = 65/2 = 32.5