Chapter 7.1, Problem 22PSC

a

To determine

The value of $m\angle H$ is to be calculated

Answer to Problem 22PSC

The value of $m\angle H={55}^0$

Explanation of Solution

Given information : The following information has been given

  $\angle E={70}^0$

JH and FH bisect the exterior angles of $\Delta JEF$

We have $\angle E={70}^0$ . Thus, now we assume that

  $\angle FJE=2j$ and $\angle JFE=2f$

Now, as JH and FH bisect the exterior angles of $\Delta JEF$ ,

  $\angle FJH={90}^0-j$ , and

  $\angle JFH={90}^0-f$

Thus, by adding up the sides of the triangle, we get

  $\angle E+2j+2f={180}^0$ , where $\angle H=j+f$

Hence, by substitution, we can say that

  $m\angle H={55}^0$

b

To determine

A formula between $m\angle H$ and $m\angle H=E$ is to be found

Answer to Problem 22PSC

The formula is $m\angle E+2m\angle H={180}^0$

Explanation of Solution

Given information : The following information has been given

  $\angle E={70}^0$

JH and FH bisect the exterior angles of $\Delta JEF$

Using the formula we got in the first part,

  $\angle E+2j+2f={180}^0$ , where $\angle H=j+f$

Hence, by substitution, we can say that

  $m\angle E+2m\angle H={180}^0$