Question

1. solve for the m∠y. 60° 130° x° y° 20° clear all 50° 40° 70° 60°

Explanation:

Step1: Find the value of \(x\)

Use the exterior - angle property of a triangle. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
If we consider the larger triangle, the exterior angle is \(130^{\circ}\), and one of the non - adjacent interior angles is \(20^{\circ}\). Let the other non - adjacent interior angle (which is \(x + 20^{\circ}\)) satisfy the equation \(130^{\circ}=(x + 20^{\circ})+\text{the angle opposite to the exterior angle}\). But using the exterior - angle property directly for the smaller part: \(x=130^{\circ}-(20^{\circ}+ \text{another angle})\). Wait, a better approach: The angle adjacent to \(130^{\circ}\) is \(180 - 130=50^{\circ}\). Then, using the angle - sum property of a triangle (the sum of angles in a triangle is \(180^{\circ}\)) for the lower triangle: \(x=50^{\circ}-20^{\circ}=30^{\circ}\).

Step2: Use the angle - sum property of a triangle for the upper - lower combined triangle

The sum of angles in a triangle is \(180^{\circ}\). Let's consider the whole figure. We know one angle is \(60^{\circ}\), and we found the adjacent angle to \(130^{\circ}\) is \(50^{\circ}\).
We use the formula \(180^{\circ}=60^{\circ}+(x + y)+20^{\circ}\). Substitute \(x = 30^{\circ}\) into the equation \(180=60+(30 + y)+20\).
First, simplify the right - hand side: \(60+30 + y+20=110 + y\).
Then, solve for \(y\): \(y=180-(60 + 30+20)=70^{\circ}\).

Answer:

\(70^{\circ}\)