∠𝐴𝐵𝐶 is bisected by 𝐵𝐷−→− . If the degree measure of ∠𝐴𝐵𝐶 is 9𝑥−5 and the degree measure of ∠𝐴𝐵𝐷 is 3𝑥+5 , find the degree measure of ∠𝐴𝐵𝐶 .

Question

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Answer 1

so ∠𝐴𝐵𝐷 = half of ∠𝐴𝐵𝐶
3x+5 = (1/2)(9x - 5)
6x + 10 = 9x - 5
-3x = -15
x = 5

∠𝐴𝐵𝐶 = 9x-5
= 9(5) - 5
= 40