Question

12 find the measure of the angle. a 125° b 210° c 235° d 180°

Explanation:

Step1: Identify the angle components

The angle is formed by a straight angle (180°) and an additional 55°? Wait, no. Wait, the angle in question: let's see the diagram. The negative x-axis to the negative y-axis is 90°, but here we have a 55° from negative x to the ray, and then the angle from positive x to the ray. Wait, no, the angle we need is the angle from the positive x-axis (standard position) going counterclockwise? Wait, no, maybe the angle is 180° + 55°? Wait, no, wait. Wait, the diagram: the ray is in the third quadrant? Wait, no, the negative x-axis, then 55° below? Wait, no, the angle between negative x and the ray is 55°, and then the angle from positive x to the ray: 180° + 55°? Wait, no, 180° (straight line) plus 55°? Wait, no, 180° is a straight line (from positive x to negative x). Then from negative x to the ray is 55°, so total angle from positive x to the ray is 180° + 55°? Wait, 180 + 55 = 235? Wait, but let's check the options. Option C is 235°. Wait, but let's re-examine. Wait, the angle between the negative x-axis and the ray is 55°, so the angle from positive x-axis (standard position, counterclockwise) would be 180° (from positive x to negative x) plus 55° (from negative x to the ray), so 180 + 55 = 235°. So that's 235°, which is option C.

Step2: Verify the calculation

180° (straight angle) + 55° = 235°. So the measure of the angle is 235°.

Answer:

C. 235°