Question

the diagram shows a triangle. angles are 4p+33°, 17p-42°, 42°. what is the value of p? p = \boxed{}°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, we set up the equation: \((4p + 33) + (17p - 42) + 42 = 180\).

Step2: Simplify the equation

Combine like terms: \(4p + 17p + 33 - 42 + 42 = 180\) → \(21p + 33 = 180\).

Step3: Solve for \(p\)

Subtract 33 from both sides: \(21p = 180 - 33 = 147\). Then divide by 21: \(p = \frac{147}{21} = 7\).

Answer:

\(p = 7\)