Question

what is the value of $p$?
there is a triangle and an exterior angle. one angle of the triangle is $p - 32^circ$, another angle of the triangle is $p - 48^circ$, and the exterior angle is $p + 7^circ$. find the value of $p$.

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two opposite interior angles, so:
$p+7^\circ=(p-32^\circ)+(p-48^\circ)$

Step2: Simplify right-hand side

Combine like terms on the right:
$p+7^\circ=2p-80^\circ$

Step3: Isolate $p$

Subtract $p$ and add $80^\circ$ to both sides:
$7^\circ+80^\circ=2p-p$
$87^\circ=p$

Answer:

$87$