The value of m∠ABD is 49° and m∠CBD is 28°.
(3x + 22) + (5x - 17) = 77°
3x + 22° + 5x - 17° = 77°
Collect like terms
3x + 5x = 77° - 22° + 17°
8x = 72°
Divide both side by 8
8x/8 = 72/8
x = 9°
Since we have gotten the value of x, we put it back into the angles given.
Therefore,
m∠ABD = 3x + 22
= 3(9) + 22 = 27° + 22° = 49°
m∠CBD = 5x - 17
= 5(9) - 17
= 45° - 17°
= 28°
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