Chapter 12.2, Problem 14E

To determine

To find:

The given angle $m\angle 1$ .

Answer to Problem 14E

  $m\angle 1={55}^0$

Explanation of Solution

Given:

  $\Delta ABC\cong \Delta QRS$

Concept used:

If two triangles are congruent.

All the corresponding parts are congruent.

If all corresponding parts of two triangles are congruent.

So the triangle are congruent.

Calculation:

The sum of the measures of the interior angles of a triangle is ${180}^0$

  $\begin{array}{l}m\angle X+m\angle Y+m\angle Z={180}^0\\ m\angle X+{80}^0+{45}^0={180}^0\\ {125}^0+m\angle X={180}^0\\ m\angle X={55}^0\end{array}$

Therefore,

The corresponding anglesis $m\angle X={55}^0$ .