Question

1. find ∠sor

135
180
90
45

Explanation:

Step1: Identify angle relationship

∠QOR is 45°, and ∠SOR is supplementary to ∠QOS (or uses vertical/linear pair). Wait, actually, ∠SOR and the 45° angle (∠QOR) are supplementary? Wait, no, first, notice that ∠POQ and ∠SOR: Wait, ∠QOR is 45°, and ∠SOR and ∠QOR are adjacent and form a linear pair? Wait, no, let's see the lines. PR is a straight line, SQ is a transversal. So ∠QOR is 45°, and ∠SOR: Wait, ∠SOR and ∠QOR are adjacent angles on a straight line? Wait, no, ∠SOP is 5x, but maybe first, notice that ∠QOR and ∠SOP are vertical angles? Wait, no, ∠QOR is 45°, and ∠SOR: Let's think about linear pairs. The angle ∠SOR and the angle adjacent to it (∠QOR) should add up to 180°? Wait, no, PR is a straight line, so the sum of angles on a straight line is 180°. So ∠QOR is 45°, and ∠SOR: Wait, ∠SOR is adjacent to ∠QOS? Wait, maybe I made a mistake. Wait, the angle ∠SOR: let's see, ∠QOR is 45°, and ∠SOR is equal to 180° - 45°? Wait, no, wait, ∠SOP is 5x, but maybe ∠QOR and ∠SOP are vertical angles? Wait, no, ∠QOR and ∠SOP: ∠QOR is 45°, ∠SOP is 5x, but maybe 5x = 45°? Wait, no, maybe ∠SOR is supplementary to ∠QOR? Wait, PR is a straight line, so ∠SOR + ∠QOR = 180°? No, that can't be, because ∠QOR is 45°, so 180 - 45 = 135. Wait, that makes sense. So ∠SOR = 180° - 45° = 135°.

Step2: Calculate ∠SOR

Since PR is a straight line, the sum of ∠QOR and ∠SOR is 180° (linear pair). So ∠SOR = 180° - 45° = 135°.

Answer:

135