Question

31 triangle sum & exterior angle theorems scavenger hunt solve for y. 72° 103° y

Explanation:

Step1: Find the value of \(x\)

Use the exterior - angle theorem. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
For the smaller triangle, \(103^{\circ}=72^{\circ}+x\).
Subtract \(72^{\circ}\) from both sides: \(x = 103^{\circ}-72^{\circ}=31^{\circ}\).

Step2: Use the triangle sum theorem

The sum of the interior angles of a large triangle is \(180^{\circ}\).
The angles of the large triangle are \(x + 28^{\circ}\), \(72^{\circ}\), and \(y\).
First, \(x + 28^{\circ}=31^{\circ}+28^{\circ}=59^{\circ}\).
Then, by the triangle sum theorem \(59^{\circ}+72^{\circ}+y=180^{\circ}\).
Combine like terms: \(131^{\circ}+y = 180^{\circ}\).
Subtract \(131^{\circ}\) from both sides: \(y=180^{\circ}-131^{\circ}\).

Answer:

\(y = 49^{\circ}\)