Question

Draw and label a diagram. QB is the angle bisector of the angle AQC. Find measure of the angle AQB if measure of angle AQC = (6x - 32)º and measure of angle AQB= (x + 16)'.

Answer 1

Since QB bisects the angle, then AQB and BQC have the same measure (that's what the little lines mean). Then we have the next equation

`\begin{gathered} m\measuredangle AQC\text{ = m}\measuredangle AQB+m\measuredangle\text{BQC} \\ m\measuredangle AQC\text{ = 2}\cdot\text{m}\measuredangle AQB \\ 6x-32=2(x+16) \end{gathered}`

Solving for x

`\begin{gathered} 6x-32=2x+32 \\ 6x-2x=32+32 \\ 4x=64 \\ x=16 \end{gathered}`

Then, the angle AQB=x+16=16+16=32. And the measure of the angle AQB is 32 degrees