Question

The measure of angle LPO is 158°. Use the diagram to complete the sentences.The measure of angle MPN is °.The measure of angle LPN is °.

Answer 1

Given:

The measure of angle LPO is 158°.

Required:

To find the angle MPN and LPN.

Step-by-step explanation:

The total angle is 158.

Therefore,

`\begin{gathered} \angle LPO=\angle LPM+\angle MPN+NPO \\ \\ 158\degree=36\degree+\angle MPN+45\degree \\ \\ \angle MPN=158\degree-36\degree-45\degree \\ \\ =77\degree \end{gathered}`

Now,

`\begin{gathered} \angle LPN=\angle LPM+\angle MPN \\ \\ \angle LPN=36\degree+77\degree \\ \\ =113\degree \end{gathered}`

Final Answer:

`\begin{gathered} \angle MPN=77\degree \\ \angle LPN=113\degree \end{gathered}`