Question

1. find b.

Explanation:

Step1: Identify angle relationship

The angle \( b \), the \( 37^\circ \) angle, and the right angle (since there's a right - angle symbol) are related such that their sum is \( 180^\circ \) (they form a straight line). But actually, since there is a right angle ( \( 90^\circ \)) between \( b \) and the \( 37^\circ \) angle? Wait, no, looking at the diagram, the three angles ( \( b \), \( 37^\circ \), and the right angle) should add up to \( 180^\circ \) because they are on a straight line. Wait, the right - angle symbol means one angle is \( 90^\circ \). So we have \( b + 37^\circ+ 90^\circ= 180^\circ \)? No, wait, maybe the right angle is between \( b \) and the other angle. Wait, actually, the angle \( b \), the \( 37^\circ \) angle, and the right angle ( \( 90^\circ \)) are complementary in the sense that \( b + 37^\circ= 90^\circ \)? Wait, no, let's think again. If there is a right - angle symbol, that means two lines are perpendicular, so the angle between them is \( 90^\circ \). So the angle \( b \) and the \( 37^\circ \) angle should add up to \( 90^\circ \) because they are part of the right angle? Wait, no, the straight line is \( 180^\circ \). Wait, the diagram shows that there is a right angle ( \( 90^\circ \)), a \( 37^\circ \) angle, and angle \( b \) on a straight line. So \( b+37^\circ + 90^\circ=180^\circ \)? No, that would be if all three are on a straight line. Wait, no, the right - angle symbol is between two lines, so the angle between those two lines is \( 90^\circ \). So angle \( b \) and the \( 37^\circ \) angle are complementary to the right angle? Wait, no, let's use the fact that the sum of angles on a straight line is \( 180^\circ \). If one of the angles is a right angle ( \( 90^\circ \)) and another is \( 37^\circ \), then \( b = 180^\circ-90^\circ - 37^\circ \)? Wait, no, maybe the right angle is between \( b \) and the \( 37^\circ \) angle. Wait, the correct approach: when two lines are perpendicular, the angle between them is \( 90^\circ \). So angle \( b \) and the \( 37^\circ \) angle are complementary, meaning \( b + 37^\circ=90^\circ \).

Step2: Solve for \( b \)

We have the equation \( b+37^\circ = 90^\circ \). To find \( b \), we subtract \( 37^\circ \) from both sides of the equation. So \( b=90^\circ - 37^\circ \).
\( b = 53^\circ \)

Answer:

\( 53^\circ \)