Question

find the value of the variables in the figure.
(5x - 7)°
(4y + 3)°
(3x + 17)°
x=
,y=
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Explanation:

Step1: Set up equation for x

Since $(5x - 7)^{\circ}$ and $(3x + 17)^{\circ}$ are vertical - angles and vertical angles are equal, we have the equation $5x-7 = 3x + 17$.
$5x-3x=17 + 7$
$2x=24$
$x = 12$

Step2: Set up equation for y

Since $(4y + 3)^{\circ}$ and $(5x - 7)^{\circ}$ are corresponding angles (assuming lines a and b are parallel) and corresponding angles are equal. Substitute $x = 12$ into $(5x - 7)^{\circ}$, we get $(5\times12-7)^{\circ}=53^{\circ}$. Then set $4y + 3=53$.
$4y=53 - 3$
$4y=50$
$y=\frac{50}{4}=12.5$

Answer:

$x = 12$, $y = 12.5$