Chapter 15.2, Problem 24PSC

To determine

To Prove: The angle is greater than the other in the given triangle.

Explanation of Solution

Given:

Point $P$ in the interior of triangle XYZ.

Formula Used:

Exterior Angle of a triangle is always greater than its remote interior angles.

Angle-Sum theorem: Sum of interior angle of a triangle is 180.

Calculation:

  

  $\begin{array}{l}\angle XPZ=\angle PZS+\angle PSZ\\ \left(\text{an exterior angle corresponding in triangle is the sum of other two angles}\right)\\ \angle PSZ=\angle Y+\angle YXS\\ \text{putting the values of }\angle \text{PSZ}\\ \angle XPZ=\angle PZS+\angle Y+\angle YXS\\ so\\ \angle XPZ>\angle Y\\ \text{hence proved}\text{.}\end{array}$

Conclusion:

Hence, Proved.