Question

calculate the measure of ∠b. circle your answer.

Explanation:

Step1: Analyze the angle relationships

Looking at the diagram, we have a right angle (90°) and two angles of 23° each, and we need to find the measure of ∠b. The sum of angles around a point or in a straight line? Wait, actually, looking at the second diagram (the one with the right angle and 23°), maybe it's a straight line with a right angle and two 23° angles. Wait, no, let's re - examine. Wait, the first diagram has a straight line, a right angle (90°), and two 23° angles. Wait, actually, the sum of angles on a straight line is 180°, but if there's a right angle and two 23° angles, maybe we are looking at a full - circle? No, wait, maybe the angle ∠b is related to the sum of angles. Wait, maybe the correct approach is: if we consider the angles around a point, but no, looking at the second diagram, there is a right angle (90°), a 23° angle, and we need to find ∠v? Wait, no, the question is about ∠b. Wait, maybe the original problem is that we have a straight line, with a right angle (90°) and two angles of 23°, and we need to find the remaining angle? Wait, no, let's do the calculation properly.

Wait, maybe the angle ∠b is calculated as follows: The sum of angles in a straight line is 180°, but if we have a right angle (90°) and two angles of 23°, no, wait, maybe it's a full angle? No, wait, let's look at the second diagram. There is a vertical line (right angle with the horizontal line), and two 23° angles on the left. Wait, maybe the angle ∠b (or ∠v) is 90° - 23°? No, that would be 67°, but that doesn't match the written answer. Wait, maybe the first diagram: the straight line has a right angle (90°), and two angles of 23°, so the total angle ∠b is 180° - 90°+23° + 23°? No, that's not right. Wait, maybe the problem is that we have a reflex angle? Wait, the written answer is 224°, let's check: 360°-(90° + 23°+23°)=360 - 136 = 224°. Ah, that makes sense. So the total angle around a point is 360°, we have a right angle (90°) and two angles of 23° each. So we subtract the sum of these angles from 360° to get ∠b.

Step2: Calculate the sum of the known angles

The known angles are 90°, 23°, and 23°. The sum of these angles is $90 + 23+23=136$ degrees.

Step3: Calculate ∠b

Since the total angle around a point is 360°, we find ∠b by subtracting the sum of the known angles from 360°. So $\angle b=360 - 136 = 224$ degrees.

Answer:

224°