Question

1. find the measure of each angle indicated. 15) 16)

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the unknown angle be \(x\).

Step2: Set up the equation for the first triangle (15)

For the triangle with angles \(35^{\circ}\), \(80^{\circ}\), and \(x\), we have the equation \(x + 35^{\circ}+80^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(x+115^{\circ}=180^{\circ}\).
Subtract \(115^{\circ}\) from both sides: \(x = 180^{\circ}-115^{\circ}\).

Step3: Set up the equation for the second triangle (16)

For the triangle with angles \(70^{\circ}\), \(70^{\circ}\), and \(y\), we have the equation \(y + 70^{\circ}+70^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(y + 140^{\circ}=180^{\circ}\).
Subtract \(140^{\circ}\) from both sides: \(y=180^{\circ}-140^{\circ}\).

Answer:

1. \(65^{\circ}\)
2. \(40^{\circ}\)