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Given that ∠ABC is bisected by BD→, m∠ABD = (-159 – 12x)°, and m∠DBC = (3x + 96)°, find x and m∠ABC.
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Given that ∠ABC is bisected by BD→, m∠ABD = (-159 – 12x)°, and m∠DBC = (3x + 96)°, find x and m∠ABC.

User Mounir Bkr
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5.6k points

1 Answer

3 votes
When anything is bisected, the two halves are equal. This means
(-159 - 12x) = (3x + 96)
-255 = 15x . . . . . . . . . . . . . add 12x-96
-17 = x

Then either of the smaller angles is
(3(-17) + 96)° = 45°

angle ABC is twice this value, or 90°.
User Yuri Malheiros
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4.8k points
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