Question

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

Explanation:

Step1: Use angle - sum property of a triangle

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

Step2: Use vertical angles property

The angle opposite to $z$ in the right - hand triangle is also $z = 60^{\circ}$ (vertical angles are equal).

Step3: Find $y$

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

Step4: Find $x$

$x = 80^{\circ}$ (vertical angles are equal, the angle opposite to the $80^{\circ}$ angle is $x$).

Step5: Calculate $x + y$

$x + y=80+50 = 130$.

Answer:

$130$