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: Apply the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(p+(p + 12)+(4p-20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((p + p+4p)+(12 - 20)=180\), which gives \(6p-8 = 180\).

Step3: Solve for \(p\)

Add \(8\) to both sides of the equation: \(6p-8 + 8=180 + 8\), so \(6p=188\). Then divide both sides by \(6\): \(p=\frac{188}{6}=\frac{94}{3}\approx31.3\).

Answer:

\(31.3\)