Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(33^{\circ}+(p + 17)^{\circ}+4p^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(33 + p+17 + 4p=180\).
\((p + 4p)+(33 + 17)=180\).
\(5p+50 = 180\).

Step3: Solve for \(p\)

Subtract 50 from both sides: \(5p+50-50=180 - 50\).
\(5p=130\).
Divide both sides by 5: \(p=\frac{130}{5}\).

Answer:

\(26\)