Question

what is the value of p?

Explanation:

Step1: Identify the angle relationship

We know that a straight line forms a \(180^\circ\) angle. The angles \(51^\circ\), \(26^\circ\), and \(p\) (along with the vertical opposite angle, but here we consider the straight line) should add up to \(180^\circ\)? Wait, no, actually, looking at the diagram, the three angles (51°, 26°, and the angle adjacent to p) are on a straight line? Wait, no, maybe the angle we need to find is the supplementary angle to the sum of 51° and 26°. Wait, let's re - examine. The straight line has angles that sum to \(180^\circ\). So the angle opposite to the combination of 51° and 26°? No, actually, the angle \(p\) and the sum of \(51^\circ+ 26^\circ\) are supplementary? Wait, no, let's think again. If we have a straight line, the sum of angles on one side of the line is \(180^\circ\). So the angle \(p\) is equal to \(180^\circ-(51^\circ + 26^\circ)\)? Wait, no, maybe the vertical angles? Wait, no, looking at the diagram, the two angles (51° and 26°) and the angle \(p\) are such that \(p\) is equal to \(180^\circ-(51^\circ+26^\circ)\)? Wait, let's calculate the sum of 51 and 26 first.

Step2: Calculate the sum of 51° and 26°

\(51^\circ+26^\circ = 77^\circ\)

Step3: Calculate the value of p

Since the angles on a straight line sum to \(180^\circ\), \(p = 180^\circ-(51^\circ + 26^\circ)=180^\circ - 77^\circ=103^\circ\)? Wait, no, maybe I got the diagram wrong. Wait, maybe the angle \(p\) is equal to \(51^\circ+26^\circ\)? No, that can't be. Wait, no, maybe the vertical angles. Wait, the straight line, so the angle adjacent to \(p\) is \(51^\circ + 26^\circ=77^\circ\), so \(p = 180^\circ-77^\circ = 103^\circ\)? Wait, no, maybe the diagram is such that \(p\) is equal to \(180-(51 + 26)\). Let's do the calculation:

First, sum of 51 and 26: \(51+26 = 77\)

Then, \(p=180 - 77=103\)? Wait, no, maybe the angle \(p\) is the sum? Wait, no, let's check again. If we have two angles 51° and 26° between two lines, and \(p\) is the angle on the straight line. Wait, maybe the correct approach is that the angle \(p\) is equal to \(180-(51 + 26)\). So:

\(51+26 = 77\)

\(p = 180 - 77=103\)

Wait, but maybe I made a mistake. Wait, another way: the angle \(p\) and the angle formed by 51° and 26° are supplementary. So \(p=180-(51 + 26)=103\).

Answer:

\(103^\circ\)