Question

homework 2: angle basics, an

1. solve for x and y (hint: using linear pair and vertical angle relationships).

(5y - 3)°
(4x - 7)°
17°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $4x - 7=17$.

Step2: Solve for x

Add 7 to both sides of the equation $4x - 7=17$: $4x=17 + 7=24$. Then divide both sides by 4, $x=\frac{24}{4}=6$.

Step3: Use linear - pair property

The sum of angles in a linear pair is $180^{\circ}$. The angle $(5y - 3)^{\circ}$ and the right - angle ($90^{\circ}$) are in a linear pair. So, $(5y-3)+90 = 180$.

Step4: Solve for y

First, simplify the left - hand side of the equation: $5y-3 + 90=5y + 87$. Then we have $5y+87 = 180$. Subtract 87 from both sides: $5y=180 - 87 = 93$. Divide both sides by 5: $y=\frac{93}{5}=18.6$.

Answer:

$x = 6,y = 18.6$