Question

a triangle has interior angle measures of 2p + 1°, 3p − 2°, and 2p − 8°. what is the value of p?
write your answer as an integer or as a decimal rounded to the nearest tenth.

p =
submit

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is \(180^\circ\). So, we set up the equation: \((2p + 1) + (3p - 2) + (2p - 8) = 180\).

Step2: Combine like terms

Combine the \(p\)-terms and constant terms: \(2p + 3p + 2p + 1 - 2 - 8 = 180\), which simplifies to \(7p - 9 = 180\).

Step3: Solve for \(p\)

Add 9 to both sides: \(7p = 180 + 9 = 189\). Then divide by 7: \(p = \frac{189}{7} = 27\).

Answer:

\(27\)