Chapter 9, Problem 25CR

To determine

Tocalculate:The measure of angleCAB .

Answer to Problem 25CR

The measure of angle CAB is ${25}^{\circ }.$

Explanation of Solution

Given information:

  $\begin{array}{l}\overline{AD}\cong \overline{DC}\\ \angle B+{50}^{\circ }=\angle DAB\end{array}$

Formula used:

The below theorem is used:

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

  

Calculation:

  

Let, $x=m\angle CAB$

By exterior angle theorem, we get

  $\angle DCA=x+\angle B$

In isosceles triangle ADC , we get

  $\angle DAC=x+\angle B$

  $\angle DAB=2x+\angle B$

But, $\angle DAB=\angle B+{50}^{\circ }$

So, $2x+\angle B=\angle B+{50}^{\circ }$

  $\begin{array}{l}2x={50}^{\circ }\\ \therefore x={25}^{\circ }\end{array}$

  $m\angle CAB={25}^{\circ }$