Question

76 triangle sum & exterior angle theorems scavenger hunt solve for x.

Explanation:

Step1: Use the exterior angle theorem for the left - hand triangle

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the left - hand triangle with exterior angle \(103^{\circ}\), we have \(x + 72^{\circ}=103^{\circ}\).

Step2: Solve for \(x\)

Subtract \(72^{\circ}\) from both sides of the equation \(x + 72^{\circ}=103^{\circ}\). So, \(x=103^{\circ}-72^{\circ}\).

Answer:

\(x = 31^{\circ}\)