Question

what is the value of p? p + 18° p + 48° p + 15° p =

Explanation:

Step1: Apply exterior - angle property of a triangle

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles.
Let's consider the triangle formed by the angles. The exterior angle is \(p + 48^{\circ}\), and the two non - adjacent interior angles are \(p+15^{\circ}\) and \(p + 18^{\circ}\). So, we can write the equation \(p + 48^{\circ}=(p + 15^{\circ})+(p + 18^{\circ})\).

Step2: Simplify the right - hand side of the equation

\((p + 15^{\circ})+(p + 18^{\circ})=p+p+15^{\circ}+18^{\circ}=2p + 33^{\circ}\). So the equation becomes \(p + 48^{\circ}=2p+33^{\circ}\).

Step3: Solve for \(p\)

Subtract \(p\) from both sides of the equation: \(p - p+48^{\circ}=2p - p+33^{\circ}\). This simplifies to \(48^{\circ}=p + 33^{\circ}\). Then subtract \(33^{\circ}\) from both sides: \(48^{\circ}-33^{\circ}=p\).

Answer:

\(p = 15^{\circ}\)