Question

(c) problem 16: (first taught in lesson 30)
find x and y.
after you enter your answer press go.
x =
y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So the angle opposite the $30^{\circ}$ angle is also $30^{\circ}$, thus $x = 30$.

Step2: Calculate $y$ using angle - sum property

In the triangle with angles $y^{\circ}$, $30^{\circ}$ and $45^{\circ}$, by the angle - sum property of a triangle ($\text{sum of angles}=180^{\circ}$), we have $y+30 + 45=180$. Then $y=180-(30 + 45)=105$. But we made a mistake above. Considering the non - overlapping part of the angles formed. The correct way is to note that the two non - overlapping angles adjacent to $y$ are $30^{\circ}$ and $45^{\circ}$. Since the sum of angles around the intersection point is $360^{\circ}$ and vertical angles are equal. We can also use the fact that in the relevant geometric figure, the angle $y$ is the sum of the non - vertical - angle parts. $y=30 + 45=75$.

Answer:

$x = 30$, $y = 75$