Question

1. calculate the measure of ∠b. circle your answer.

Explanation:

Step1: Identify angle relationship

The angle of \(23^\circ\), \(\angle b\), and the right angle (\(90^\circ\)) are on a straight line, so their sum is \(180^\circ\) (supplementary angles). But actually, looking at the right diagram, the \(23^\circ\) angle, \(\angle b\), and the right angle form a right - angled situation? Wait, no, the straight line is \(180^\circ\), and there is a right angle (\(90^\circ\)) and a \(23^\circ\) angle and \(\angle b\). Wait, more accurately, in the right - angled part, the sum of \(23^\circ\), \(\angle b\), and \(90^\circ\)? No, looking at the diagram, the horizontal line is a straight line, and there is a vertical line (forming a right angle) and a \(23^\circ\) angle. So the sum of \(23^\circ\), \(\angle b\), and \(90^\circ\) is not correct. Wait, actually, the angle between the horizontal line and the vertical line is \(90^\circ\), and the \(23^\circ\) angle and \(\angle b\) are complementary to the right angle? Wait, no. Let's think again. The three angles: \(23^\circ\), \(\angle b\), and \(90^\circ\) are on a straight line? No, the straight line is \(180^\circ\). Wait, the vertical line is perpendicular to the horizontal line, so the angle between them is \(90^\circ\). The \(23^\circ\) angle and \(\angle b\) are such that \(23^\circ+\angle b + 90^\circ=180^\circ\)? No, that would be if they are on a straight line. Wait, no, the correct relationship is that \(23^\circ+\angle b=90^\circ\) (because they are complementary angles, since the vertical line is perpendicular to the horizontal line, forming a right angle). So \(\angle b = 90^\circ - 23^\circ\).

Step2: Calculate \(\angle b\)

\(\angle b=90^{\circ}- 23^{\circ}=67^{\circ}\)

Answer:

\(67^{\circ}\)