Question

1. given the following diagram, what are the values of x and y? y° (17x + 21)° 123° x = _______ y = _______

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $y = 123$ since $y$ and the $123^{\circ}$ angle are vertical angles.

Step2: Use linear - pair property

The angle $(17x + 21)^{\circ}$ and the $123^{\circ}$ angle form a linear - pair, so their sum is $180^{\circ}$. We set up the equation $17x+21 + 123=180$.
First, simplify the left - hand side: $17x+144 = 180$.
Then, subtract 144 from both sides: $17x=180 - 144$, so $17x = 36$.
Finally, divide both sides by 17: $x=\frac{36}{17}$.

Answer:

$x=\frac{36}{17}, y = 123$