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Ray BD bisects /_ABC. If m/_ABD=(7x-9)^(@) and m/_CBD=(2x+36)^(@), what is the m/_ABC ? A. 54^(@) B. 132^(@) C. 86^(@) D. 108^(@)

22. Ray BD \mathrm{BD} bisects ∠ABC \angle \mathrm{ABC} . If m∠ABD=(7x−9)∘ \mathrm{m} \angle \mathrm{ABD}=(7 \mathrm{x}-9)^{\circ} and m∠CBD=(2x+36)∘ \mathrm{m} \angle \mathrm{CBD}=(2 \mathrm{x}+36)^{\circ} , what is the m∠ABC \mathrm{m} \angle \mathrm{ABC} ?\newlineA. 54∘ 54^{\circ} \newlineB. 132∘ 132^{\circ} \newlineC. 86∘ 86^{\circ} \newlineD. 108∘ 108^{\circ}

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Full solution

Q. 22. Ray BD \mathrm{BD} bisects ∠ABC \angle \mathrm{ABC} . If m∠ABD=(7x−9)∘ \mathrm{m} \angle \mathrm{ABD}=(7 \mathrm{x}-9)^{\circ} and m∠CBD=(2x+36)∘ \mathrm{m} \angle \mathrm{CBD}=(2 \mathrm{x}+36)^{\circ} , what is the m∠ABC \mathrm{m} \angle \mathrm{ABC} ?\newlineA. 54∘ 54^{\circ} \newlineB. 132∘ 132^{\circ} \newlineC. 86∘ 86^{\circ} \newlineD. 108∘ 108^{\circ}
  1. Identify Relationship: Identify the relationship between the angles since BDBD bisects angle ABCABC, meaning angle ABDABD equals angle CBDCBD.
  2. Solve Equation: Solve the equation to find the value of xx.
  3. Substitute xx: Substitute x=9x = 9 back into either angle's expression to find the measure of angle ABDABD or CBDCBD.
  4. Find Angle Measures: Since BDBD bisects angle ABCABC, angle ABCABC is twice the measure of angle ABDABD.

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