Chapter 9, Problem 28CR

To determine

Tocalculate:The measure of angleJ .

Answer to Problem 28CR

The measure of angle J is ${45}^{\circ }.$

Explanation of Solution

Given information:

  $\begin{array}{l}\overline{GH}\cong \overline{GJ}\\ \angle 1={(}^3\\ \angle 2=x^{\circ }\end{array}$

Formula used:

The below properties are used:

If the angles are supplementary, then they are equal.

In isosceles triangle, base angles are equal.

Calculation:

  

If the angles are supplementary, then they are equal.

  $\angle 1$ issupplementary to $\angle 2$ ,so

  $\begin{array}{l}3x+x={180}^{\circ }\\ \therefore 4x={180}^{\circ }\\ \therefore x={45}^{\circ }\end{array}$

Since $\overline{GH}\cong \overline{GJ}$ , $\Delta GHJ$ is an isosceles triangle.

  $\begin{array}{l}\angle J\cong \angle 2\\ \therefore m\angle J={45}^{\circ }\end{array}$