Chapter 7.4, Problem 19PPS

To determine

To calculate:

The value of $x$ if $\overline{JH},\overline{JP},\overline{PH}$ are mid-segments of $△KLM$

Answer to Problem 19PPS

The value of $x$ is $60°$

Explanation of Solution

Given information:

  

Calculation:

Here, $\overline{JH},\overline{JP},\overline{PH}$ are mid-segments of $△KLM$ .

As per the triangle mid-segment theorem:

  $\overline{PH}\parallel \overline{KL}$

And as per the alternate interior angles theorem:

  $\angle PHM\cong \angle JLK$

According to definition of congruence for $△KLM$ and $△JHP$

  $\begin{array}{l}m\angle PJH\cong m\angle JHL\\ 44°=m\angle JHL\\ m\angle JHL=44°\end{array}$

Use the sum of angle of triangle theorem for calculating value of $x$

  $\begin{array}{l}x+76°+44°=180°\\ x=180°-120°\\ x=60°\end{array}$