Answer:
63°
Step-by-step explanation:
Without a diagram, we have to assume that ray BC lies between BA and BD. Then the angle addition theorem tells you ...
m∠ABC + m∠CBD = m∠ABD
(7x -9°) + (6x +27°) = 96° . . . . . . substitute the given angle measures
13x +18° = 96° . . . . . . . . . . . . . . . simplify
13x = 78° . . . . . . . . . . . . . . . . . . . subtract 18°
x = 78°/13 = 6° . . . . . . . . . . . . . . divide by the coefficient of x
Then the angle of interest is ...
m∠CBD = (6x +27°) = 6(6°) +27° . . . . . substitute the value of x into 6x+27°
m∠CBD = 63°
