Question

10 what is the value of p? a. 125° b. 35° c. 45° d. 55°

Explanation:

Step1: Find the adjacent angle to 125°

The angle adjacent to 125° on a straight line is \(180^\circ - 125^\circ = 55^\circ\).

Step2: Use the triangle angle sum property

In a triangle, the sum of angles is \(180^\circ\). We know one angle is \(90^\circ\) (right angle) and another is \(55^\circ\) (from step 1). So \(p = 180^\circ - 90^\circ - 55^\circ = 35^\circ\)? Wait, no, wait. Wait, maybe the triangle has angles: let's re - check. Wait, the straight line angle: the angle inside the triangle adjacent to 125° is \(180 - 125 = 55^\circ\). Then the other angle is 90°? Wait, no, maybe the triangle has a 90° angle? Wait, no, maybe I made a mistake. Wait, let's do it again. The exterior angle is 125°, so the interior angle is \(180 - 125 = 55^\circ\). Then the triangle has angles: 90° (wait, the diagram has a right angle? Wait, the diagram shows a triangle with one angle as 90°? Wait, no, maybe the triangle has angles: let's see, the sum of angles in a triangle is 180. If one angle is 90°, another is 55°, then \(p = 180 - 90 - 55 = 35\)? Wait, but wait, maybe the triangle is not right - angled. Wait, the diagram has a 90° mark? Wait, the original diagram: the triangle has a 90° angle (the little square), so it's a right - triangle. So the two non - right angles sum to 90°. Wait, no, the angle adjacent to 125° is 55°, so then \(p = 90 - 55 = 35\)? Wait, no, wait. Wait, the exterior angle is 125°, so the interior angle is 55°, then in the right - triangle, the other non - right angle is \(p\), so \(p + 55 = 90\), so \(p = 35\). So the answer is 35°, which is option B.

Answer:

B. 35°