Chapter 51, Problem 1A

Determine the values of ∠2, ∠3, and ∠4 if ∠l is 113°.

To determine

The value of angles $\angle 2,\angle 3,\text{and }\angle 4$ for the given value of $\angle 1=113°$.

Answer to Problem 1A

The values of angles are

  $\begin{array}{l}\angle 2=67°\\ \angle 3=113°,\text{and}\\ \angle 4=67°\end{array}$.

Explanation of Solution

Given:

The following figure is given

The angles $\angle 1\text{and }\angle 3$ are opposite angles. The opposite angles are equal, so, the angle $\angle 3\text{= 11}3°$

Now, angle 2 and angle 1 together make a straight line. The angle of straight line is 180^o. Thus, the value of angle 2 can be calculated as

  $\begin{array}{l}\angle 2+\angle 1=180°\\ \angle 2+113°=180°\\ \angle 2=180°-113°\\ \angle 2=67°\end{array}$

The angles $\angle 2\text{and }\angle 4$ are opposite angles. The opposite angles are equal, so, the angle $\angle 4\text{= 67}°$