Question

question 8 of 10
what is the value of p?
140°
p° 90°
a. 50°
b. 40°
c. 90°
d. 60°

Explanation:

Step1: Identify triangle angle sum

In a triangle, the sum of angles is \(180^\circ\). We also use the linear pair (supplementary angles) for the \(140^\circ\) angle. The supplementary angle to \(140^\circ\) is \(180^\circ - 140^\circ = 40^\circ\).

Step2: Calculate \(p\)

The triangle has a right angle (\(90^\circ\)) and the angle we found (\(40^\circ\)). So, \(p = 180^\circ - 90^\circ - 40^\circ = 50^\circ\)? Wait, no—wait, maybe the triangle has angles: the angle adjacent to \(140^\circ\) is \(40^\circ\) (linear pair), the right angle \(90^\circ\), so \(p = 180 - 90 - 40 = 50\)? Wait, no, maybe I mixed up. Wait, the triangle: one angle is \(90^\circ\), one angle is \(180 - 140 = 40^\circ\) (since \(140^\circ\) and that angle are supplementary), so the third angle \(p\) is \(180 - 90 - 40 = 50\)? Wait, but let's check again. Wait, maybe the triangle is formed with the \(140^\circ\) angle's supplement. So linear pair: \(180 - 140 = 40^\circ\). Then, in the right - angled triangle, angles sum to \(180\), so \(p + 90 + 40 = 180\), so \(p = 180 - 90 - 40 = 50\)? Wait, but the options have A as \(50^\circ\), B as \(40^\circ\), etc. Wait, maybe I made a mistake. Wait, no—wait, maybe the triangle is such that the angle opposite? Wait, no, let's re - examine the diagram. The diagram has two intersecting lines, one forming a \(140^\circ\) angle, and a right angle (\(90^\circ\)) in the triangle. So the three angles of the triangle: one is \(90^\circ\), one is \(180 - 140 = 40^\circ\) (since \(140^\circ\) and that angle are supplementary), so the third angle \(p\) is \(180 - 90 - 40 = 50^\circ\). Wait, but let's check the options. Option A is \(50^\circ\). Wait, but maybe I messed up the linear pair. Wait, no, linear pair: two angles on a straight line sum to \(180^\circ\), so \(140 + x = 180\), so \(x = 40\). Then in the right - angled triangle, angles are \(90\), \(40\), and \(p\). So \(p = 180 - 90 - 40 = 50\). So the correct answer should be A. \(50^\circ\). Wait, but wait, maybe the triangle is different. Wait, maybe the angle adjacent to \(140^\circ\) is \(40^\circ\), and the triangle has angles \(40^\circ\), \(90^\circ\), and \(p\). So \(p = 180 - 90 - 40 = 50\). So the answer is A. \(50^\circ\).

Answer:

A. \(50^\circ\)