Question

what is the value of p? the triangle has angles ( p - 5^circ ), ( p ), and an exterior angle ( p + 48^circ ). find ( p ). ( p = ) ( ^circ ) submit

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(p + 48=(p - 5)+p\)

Step2: Simplify the equation

First, expand the right - hand side: \(p + 48=p - 5+p\)
Combine like terms on the right - hand side: \(p + 48 = 2p-5\)
Subtract \(p\) from both sides: \(p + 48-p=2p - 5-p\)
We get: \(48=p - 5\)

Step3: Solve for p

Add 5 to both sides of the equation: \(48 + 5=p-5 + 5\)
So, \(p=53\)

Answer:

\(53\)