# How do I solve this?

May 16, 2016

$\angle M P L = {80}^{o}$

#### Explanation:

Join line $M N$ and now examine $\Delta M N P$.

As $m \hat{M L} = {175}^{o}$ and $m \hat{O N} = {15}^{o}$

$\angle M P L = \angle M N L - \angle P M N$,

as exterior angle is equal to sum of interior opposite angles.

Now $\angle M N L = \frac{1}{2} \times \left(m \hat{M L}\right) = \frac{1}{2} \times {175}^{o}$ and

$\angle P M N = \frac{1}{2} \times \left(m \hat{O N}\right) = \frac{1}{2} \times {15}^{o}$

Hence $\angle M P L = \angle M N L - \angle P M N$

= $\frac{1}{2} \times {175}^{o} - \frac{1}{2} \times {15}^{o}$

= $\frac{1}{2} \times \left({175}^{o} - {15}^{o}\right)$

= ${80}^{o}$

May 16, 2016

$\angle M P L = \frac{\angle M L}{2} - \frac{\angle O N}{2} = {80}^{o}$

#### Explanation:

$\angle O M N = \frac{\angle O N}{2}$
$\angle M N L = \frac{\angle M L}{2}$
$\angle M P L + \pi - \angle M N L + \angle O M N = \pi$
Solving for $\angle M P L = \frac{\angle M L}{2} - \frac{\angle O N}{2} = {80}^{o}$