Chapter 7.1, Problem 11PSA

To determine

To find:The values of $m\angle ORP$ and $m\angle MOR$

Answer to Problem 11PSA

The values are $\angle MOR={50}^0$ and $\angle ORP={40}^0$

Explanation of Solution

Given information:The following information has been given

  $\angle P={10}^0$

  $\angle M={90}^0$

RO bisects the angle MRP

Formula used:The sum of the angles in any triangle is ${180}^0$

Calculation:We know that in triangle MRP,

  $\angle P={10}^0$

  $\angle M={90}^0$

Hence, we can say that

  $\angle R={180}^0-({90}^0+{10}^0)={80}^0$

Now, as RO bisects the angle MRP, we can say that

  $\angle ORP=\angle ORM=\frac{1}{2}({80}^0)={40}^0$

Thus, we know that

  $\angle ORP={40}^0$

Now, in triangle MOR, we know that

  $\angle ORM={40}^0$

  $\angle M={90}^0$

Thus, we can say that

  $\angle MOR={180}^0-({90}^0+{40}^0)={50}^0$

Hence, we know that

  $\angle MOR={50}^0$