Chapter 5.3, Problem 17PSB

To determine

To Find: The value of $m\angle \text{DAB}$ .

Answer to Problem 17PSB

  $m\angle DAB={60}^{\circ }$

Explanation of Solution

Given:

  

  $\overleftrightarrow{DA}\parallel \overleftrightarrow{BC}\text{ and }△\text{ABC is an equilateral triangle}\text{.}$

Concept Used:

If two lines are parallel intersected by a transversal alternate interior angles are equal. Sum of angles formed by a straight line is $180°$

Calculation:

Here, we have

  

  $\overleftrightarrow{DA}\parallel \overleftrightarrow{BC}\text{ and }△\text{ABC is an equilateral triangle}\text{.}$

  $\begin{array}{l}\Rightarrow \angle DAB\cong \angle CBA\left(\text{Alternate interior angles}\right)\\ \because m\angle CBA={60}^{\circ }\\ \Rightarrow m\angle DAB={60}^{\circ }\end{array}$