Question

If MQ also bisects angle ∠LMP, find the measure of ∠QMP and find the value of x. ∠QMP = (5x + 10)º

Answer 1

Explanation:

If MQ also bisects angle ∠LMP, then;

<LMQ + <QMP = <LMP

Also <LMQ = <QMP

The equation becomes <QMP + <QMP = <LMP

2<QMP = <LMP

Let <LMP be 8x+40° (This is an assumed value)

2(5x+10) = 8x+40

Open the parenthesis

10x+20 = 8x+40

10x-8x = 40-20

2x = 20

x = 20/2

x = 10

Find <QMP

Since <QMP = 5x+10

<QMP = 5(10)+10

<QMP = 50+10

<QMP = 60 degrees

Note that the angle <LMP was assumed. Any other function can be used depending on the question