Question

1. art the drawing below shows the side view of a drawing easel. the brace is parallel to the ground. if ( mangle a ) is ( 82^circ ), what is the measure of ( angle b )?

Explanation:

Step1: Identify the relationship

Since the brace is parallel to the ground, ∠A and ∠B are same - side interior angles with respect to the transversal (the side of the easel). And we know that for two parallel lines cut by a transversal, same - side interior angles are supplementary. That is, \(m\angle A + m\angle B=180^{\circ}\).

Step2: Solve for \(m\angle B\)

We are given that \(m\angle A = 82^{\circ}\). Substitute this value into the equation \(m\angle A + m\angle B = 180^{\circ}\).
So, \(82^{\circ}+m\angle B=180^{\circ}\).
To find \(m\angle B\), we subtract \(82^{\circ}\) from both sides of the equation: \(m\angle B=180^{\circ}- 82^{\circ}\).
\(m\angle B = 98^{\circ}\)

Answer:

The measure of \(\angle B\) is \(98^{\circ}\)