Question

find the value of x. if bd is an angle bisector of ∠abc, and m∠abc = 122°, and m∠abd = 8x - 3

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal parts. So, if \(BD\) is the angle - bisector of \(\angle ABC\), then \(m\angle ABD=\frac{1}{2}m\angle ABC\).

Step2: Substitute the given values

We know that \(m\angle ABC = 122^{\circ}\) and \(m\angle ABD=8x - 3\). So, \(8x - 3=\frac{1}{2}\times122\).

Step3: Simplify the right - hand side

\(\frac{1}{2}\times122 = 61\). So the equation becomes \(8x-3 = 61\).

Step4: Solve for \(x\)

Add 3 to both sides of the equation: \(8x-3 + 3=61 + 3\), which gives \(8x=64\). Then divide both sides by 8: \(x=\frac{64}{8}=8\).

Answer:

8