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, \((3p - 10)+(4p + 4)+(p+18)=180\).

Step2: Combine like - terms

First, expand the left - hand side: \(3p-10 + 4p+4 + p+18=(3p + 4p+p)+(-10 + 4+18)\).
\(3p+4p + p=8p\) and \(-10 + 4+18 = 12\). So the equation becomes \(8p+12 = 180\).

Step3: Solve for \(p\)

Subtract 12 from both sides of the equation: \(8p+12-12=180 - 12\), which gives \(8p=168\).
Then divide both sides by 8: \(p=\frac{168}{8}\).

Answer:

\(p = 21\)