Chapter 7.1, Problem 8PSA

To determine

To find:The values of $m\angle H$ , $m\angle HGJ$ and $m\angle HJG$

Answer to Problem 8PSA

The values are $m\angle H={20}^0$ , $m\angle HJG={70}^0$ and $m\angle HGJ={90}^0$

Explanation of Solution

Given information:The following information has been given

G and J are the midpoints of FH and HK respectively

Formula used

: parallel lines subtend equal angles, hence form similar triangles

Calculation:By the midline theorem, we can say that

  $m\angle HGJ=m\angle HFK={90}^0$

Thus, we know that

  $m\angle HGJ={90}^0$

Also, we can say that

  $m\angle HJG=m\angle HKF={70}^0$

Thus, we know that

  $m\angle HJG={70}^0$

Now, in triangle HGJ, we can say that

  $m\angle H={180}^0-({70}^0+{90}^0)={20}^0$

Thus, we know that

  $m\angle H={20}^0$