Question

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

Explanation:

Step1: Use the angle - bisector property

Since \(BD\) is the angle bisector of \(\angle ABC\), we have \(m\angle ABD=m\angle DBC\). And \(m\angle ABC = m\angle ABD+m\angle DBC\). Given \(m\angle ABC = 122^{\circ}\), then \(m\angle ABD=\frac{1}{2}m\angle ABC\).
Also, \(m\angle ABD = 8x−3\). So, \(8x−3=\frac{1}{2}\times122\).

Step2: Solve the equation for \(x\)

First, simplify the right - hand side of the equation \(8x−3=\frac{1}{2}\times122\). We know that \(\frac{1}{2}\times122 = 61\). Then the equation becomes \(8x−3 = 61\).
Add \(3\) to both sides of the equation: \(8x-3 + 3=61 + 3\), which gives \(8x=64\).
Divide both sides by \(8\): \(x=\frac{64}{8}\).

Answer:

\(x = 8\)