problem 19: (first taught in lesson 31) find x + y. after you enter your answer press go. x + y =

Answer:

$180$

Explanation:

Step1: Use angle - sum property of a triangle

In the left - hand triangle, the third angle (let's call it $a$) is $180-(80 + 40)=60^{\circ}$.

Step2: Use vertical angles

The vertical angle to $a$ in the right - hand triangle is also $60^{\circ}$.

Step3: Find $y$

In the right - hand triangle, using the angle - sum property of a triangle, $y=180-(70 + 60)=50^{\circ}$.

Step4: Find $x$

$x = 130^{\circ}$ (since the angle adjacent to the $50^{\circ}$ angle in a linear pair).

Step5: Calculate $x + y$

$x + y=130+50 = 180$.