Question

what is the measure of angle 3 in degrees?
27°
33°
60°
153°

Explanation:

Step1: Find angle adjacent to 93° and 60°

The sum of angles around a point is 180° (linear pair or straight line). So, the angle adjacent to 93° and 60° (let's call it angle x) is $180 - 93 - 60 = 27°$? Wait, no, wait. Wait, actually, the angle between r and the line with 60°: wait, maybe first, the angle opposite to the 93°? Wait, no, let's look at the triangle. The triangle has angles: one is 60°, one is related to the 93°, and angle 3. Wait, the straight line: the angle between the line p (horizontal) and the line with angle 93° and 60°: the sum of 60°, 93°, and the angle vertical to angle 3? Wait, no, maybe the angle at the intersection: the three angles (60°, 93°, and the angle that is vertical to angle 3) should add up to 180°? Wait, no, around a point, the sum is 360°, but linear pairs are 180°. Wait, let's re-examine. The horizontal line p, and the two lines (one with 60°, one with 93°) meet at a point. So, the angle between the 60° line and the 93° line: let's call that angle A. Then, 60° + 93° + angle A = 180°? No, that can't be. Wait, no, the horizontal line is straight, so the sum of angles on one side of the line is 180°. So, 60° + (angle between 60° and 93°) + 93°? No, maybe I'm overcomplicating. Wait, the angle that is vertical to angle 3: let's see, the triangle has angles: 60°, angle 1, and angle 3? Wait, no, the lines q is parallel to p? Wait, p and q are both horizontal, so they are parallel. So, the transversal creates alternate interior angles. Wait, maybe the angle at the top: the angle between r and s is 93°, and the angle between p and the line with 60° is 60°, so the angle between r and p: let's calculate the angle between r and p. Since the line p is straight, the angle between r and p would be 180° - 93° - 60°? Wait, 93° + 60° = 153°, so 180° - 153° = 27°. Then, since p and q are parallel, angle 3 is equal to that 27°? Wait, no, maybe alternate interior angles. Wait, if p || q, then the angle alternate to the 27° angle would be angle 3. Wait, but let's check the options. The options are 27°, 33°, 60°, 153°. Wait, 93° + 60° = 153°, so 180° - 153° = 27°. Then angle 3 is 27°? Wait, but let's confirm. The sum of angles in a triangle: if the triangle has angles 60°, angle 1, and angle 3, but angle 1 is vertical to the angle that is 180° - 60° - 93°? Wait, no, maybe the angle at the intersection: 60° + 93° + x = 180°, so x = 180 - 60 - 93 = 27°. Then, since p and q are parallel, angle 3 is equal to x (alternate interior angles), so angle 3 is 27°. Wait, but let's check the options. One of the options is 27°, so that's the answer.

Step2: Confirm with parallel lines

Since lines p and q are parallel (both horizontal), the transversal (the line with angle 3) creates alternate interior angles. The angle we calculated (27°) is alternate to angle 3, so angle 3 = 27°.

Answer:

27°