Question

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

Explanation:

Step1: Use the triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(6p + 9p+75^{\circ}=180^{\circ}\).

Step2: Combine like terms

Combine \(6p\) and \(9p\). We get \(15p + 75^{\circ}=180^{\circ}\).

Step3: Isolate the term with \(p\)

Subtract \(75^{\circ}\) from both sides: \(15p=180^{\circ}- 75^{\circ}\), so \(15p = 105^{\circ}\).

Step4: Solve for \(p\)

Divide both sides by \(15\): \(p=\frac{105^{\circ}}{15}\).

Answer:

\(7\)