Question

the diagram shows a triangle. what is the value of p? write your answer as an integer or as a decimal rounded to the nearest tenth. p = □°

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(2p + 2p+(2p + 7)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2p+2p + 2p+7=(2 + 2+2)p+7=6p + 7\). The equation becomes \(6p+7 = 180\).

Step3: Solve for \(p\)

Subtract 7 from both sides: \(6p=180 - 7=173\). Then divide both sides by 6: \(p=\frac{173}{6}\approx28.8\).

Answer:

\(28.8\)