Chapter 1.5, Problem 2PSA

a.

To determine

To Find: The congruent angles .

Answer to Problem 2PSA

  $\angle NRO\text{ and }\angle PRO\text{are congruent angles}\text{. }$

Explanation of Solution

Given:

  

  $\Rightarrow \overline{RO}\text{ bisect }\angle NRP$

Concept Used:

Bisector of angle divides the angle into two equal parts.

Calculation:

Here, we have

  $\begin{array}{l}\Rightarrow \overline{RO}\text{ bisect }\angle NRP\\ \Rightarrow m\angle NRO=m\angle PRO\\ \Rightarrow \angle NRO\cong \angle PRO\end{array}$

Conclusion:

  $\angle NRO\cong \angle PRO$

b.

To determine

To Find: The congruent angles .

Answer to Problem 2PSA

  $\angle SXT,\angle TXV\text{and}\angle WXV\text{are congruent angles}\text{. }$

Explanation of Solution

Given:

  

  $\Rightarrow \overline{XT}\text{ and }\overline{XV}\text{ trisect }\angle SXW$

Concept Used:

Trisector of angle divides the angle into three equal parts.

Calculation:

Here, we have

  $\begin{array}{l}\Rightarrow \overline{XT}\text{ and }\overline{XV}\text{ trisect }\angle SXW\\ \Rightarrow m\angle SXT=m\angle TXV=m\angle WXV\\ \Rightarrow \angle NRO\cong \angle PRO\\ \Rightarrow \angle SXT\cong \angle TXV\cong \angle WXV\end{array}$

Conclusion:

  $\angle SXT\cong \angle TXV\cong \angle WXV$