Question

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

Explanation:

Step1: Find the third - angle in the left - hand triangle

The sum of angles in a triangle is $180^{\circ}$. In the left - hand triangle with angles $80^{\circ}$ and $40^{\circ}$, the third angle $z$ is $180-(80 + 40)=60^{\circ}$.

Step2: Use the vertical - angle property

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

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

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

Step4: Find $x$

The angle $x$ and the $40^{\circ}$ angle are vertical angles, so $x = 40^{\circ}$.

Step5: Calculate $x + y$

$x + y=40+50 = 130^{\circ}$.

Answer:

$130$