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Given m/_ABD is a straight angle. {:[m/_ABC=8x-41^(@)],[m/_CBD=9x+17^(@)]:} Find m/_CBD :

Given\newlinem∠ABD m \angle A B D is a straight angle.\newlinem∠ABC=8x−41∘m∠CBD=9x+17∘ \begin{array}{l} m \angle A B C=8 x-41^{\circ} \\ m \angle C B D=9 x+17^{\circ} \end{array} \newlineFind m∠CBD m \angle C B D :

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Full solution

Q. Given\newlinem∠ABD m \angle A B D is a straight angle.\newlinem∠ABC=8x−41∘m∠CBD=9x+17∘ \begin{array}{l} m \angle A B C=8 x-41^{\circ} \\ m \angle C B D=9 x+17^{\circ} \end{array} \newlineFind m∠CBD m \angle C B D :
  1. Identify Angle ABD: Since ABD is a straight angle, m∠ABD=180∘m\angle ABD = 180^\circ.
  2. Calculate Angle ABD: Add the measures of angles ABC and CBD to get the measure of angle ABD.\newlinem/_ABD=m/_ABC+m/_CBDm/\_ABD = m/\_ABC + m/\_CBD\newline180=(8x−41)+(9x+17)180 = (8x - 41) + (9x + 17)
  3. Solve for x: Combine like terms to solve for x.\newline180=17x−24180 = 17x - 24

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