Question

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

Explanation:

Step1: Use the triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \((p - 3)+3p + 39=180\).

Step2: Simplify the left - hand side

Combine like terms: \(p-3 + 3p+39=(p + 3p)+(-3 + 39)=4p+36\). The equation becomes \(4p + 36=180\).

Step3: Solve for \(p\)

Subtract 36 from both sides: \(4p=180 - 36\), so \(4p=144\). Then divide both sides by 4: \(p=\frac{144}{4}\).

Answer:

\(p = 36\)