Question

Find m angle MON There is a model in the photo

Answer 1

$m \angle M O N=89^{\circ}$

Solution:

Given $m \angle L O N$ is a straight angle.

$m \angle M O N=3 x+89^{\circ}$

$m \angle L O M=8 x+58^{\circ}$

To find the value of $m \angle M O N$:

Sum of the adjacent angles in a straight line = 180°

$m \angle M O N+m \angle L O M=180^{\circ}$

$\begin{aligned}&3 x+89^{\circ}+8 x+58^{\circ}=180^{\circ}\\&11 x+147^{\circ}=180^{\circ}\\&11 x=180^{\circ}-147^{\circ}\\&11 x=33^{\circ}\end{aligned}$

$x=3^{\circ}$

Substitute x = 3° in $m \angle M O N$.

$m \angle M O N=3 (3^{\circ})+89^{\circ}$

                $=9^{\circ}+89^{\circ}$

                $=98^{\circ}$

$m \angle M O N=89^{\circ}$

Hence m∠MON = 89°.