Question

the diagram shows a triangle. what is the value of p?

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((2p - 44)+(2p - 16)+32 = 180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((2p+2p)+(-44 - 16 + 32)=180\).
\(4p+(-28)=180\), which is \(4p-28 = 180\).

Step3: Solve for \(p\)

Add \(28\) to both sides of the equation: \(4p-28 + 28=180 + 28\).
We get \(4p=208\).
Divide both sides by \(4\): \(p=\frac{208}{4}\).

Answer:

\(p = 52\)