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, \(34^{\circ}+2p+(p - 22^{\circ})=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(34^{\circ}-22^{\circ}+2p + p=180^{\circ}\), which gives \(12^{\circ}+3p=180^{\circ}\).

Step3: Solve for \(p\)

Subtract \(12^{\circ}\) from both sides: \(3p=180^{\circ}-12^{\circ}=168^{\circ}\). Then divide both sides by \(3\): \(p=\frac{168^{\circ}}{3}=56^{\circ}\).

Answer:

\(56\)