Question

(c) problem 17: (first taught in lesson 31)
find x and y.

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $115^{\circ}=45^{\circ}+5x^{\circ}$.

Step2: Solve for $x$

Subtract $45^{\circ}$ from both sides of the equation $115 = 45 + 5x$. We get $115-45=5x$, then $70 = 5x$, and $x=\frac{70}{5}=14$.

Step3: Use linear - pair property

The angle $2y^{\circ}$ and the exterior angle $115^{\circ}$ form a linear pair. So, $2y+115 = 180$.

Step4: Solve for $y$

Subtract $115$ from both sides of the equation $2y+115 = 180$. We get $2y=180 - 115=65$, then $y=\frac{65}{2}=35$.

Answer:

$x = 14$, $y = 35$