Question

problem 19: find x + y. (first taught in lesson 31)

Explanation:

Step1: Use vertical - angle property

The vertical angles are equal. The non - labeled angle in the left - hand triangle opposite the $40^{\circ}$ angle is also $40^{\circ}$.

Step2: Find $x$ in the left - hand triangle

In the left - hand triangle, using the angle - sum property of a triangle ($180^{\circ}$ in a triangle). So $x=180-(80 + 40)=60^{\circ}$.

Step3: Find $y$ in the right - hand triangle

In the right - hand triangle, using the angle - sum property of a triangle. So $y=180-(70 + 40)=70^{\circ}$.

Step4: Calculate $x + y$

$x + y=60+70 = 130^{\circ}$.

Answer:

$130^{\circ}$