Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(36+(p + 32)+13p=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(36 + p+32+13p=180\), which becomes \((1 + 13)p+(36 + 32)=180\), or \(14p+68 = 180\).

Step3: Isolate the term with \(p\)

Subtract \(68\) from both sides: \(14p=180 - 68\). So, \(14p=112\).

Step4: Solve for \(p\)

Divide both sides by \(14\): \(p=\frac{112}{14}\).

Answer:

\(p = 8\)