Question

If m∠BAD = 65, what is the m∠DCB?

Answer 1

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Answer 2

Since AB = BD, angle BAD = angle BDA = 65 degrees.
Equal sides have equal angles opposite them
In a triangle,the sum of all angles is 180 degrees.
Therefore, angle DBA = 180 - 65 -65 = 50
In a triangle, the external angle is equal to the sum of opposite interior angles,
Therefore, angle BDC = angle BAD + angle ABD = 65 + 50 = 115
In triangle BDC, BD = DC, therefore angle DBC = angle DCB
Therefore, angle DBC + angle DCB +angle BDC = 180
2*angle DCB = 180-115
angle DCB = 65/2 = 32.5 degrees