Chapter 1.6, Problem 8PSB

To determine

To Prove: If an obtuse angle is bisected each of the two resulting angles is acute.

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle JKH\text{is an obtuse angle}\\ \overrightarrow{LK}\text{ bisects }\angle JKH\end{array}$

Concept Used:

Bisectors divides the angle into two equal parts.

Proof:

Here, we have

  $\begin{array}{l}\angle JKH\text{is an obtuse angle}\\ \Rightarrow 90°<\angle JKH<180°\\ \Rightarrow \frac{1}{2}\left(90°\right)<\frac{1}{2}\left(\angle JKH\right)<\frac{1}{2}\left(180°\right)\\ \Rightarrow 45°<\left(\angle JKL\right)<90°\\ \Rightarrow 45°<\left(\angle HKL\right)<90°\\ \angle JKL\text{ and }\angle HKL\text{ are acute angles}\text{.}\end{array}$