Question

find the values of x and y. (5y)° (2y + 12)° (5x)° x = y =

Explanation:

Step1: Set up equation for y

Since the sum of angles on a straight - line is 180 degrees, and the angles $(5y)^{\circ}$ and $(2y + 12)^{\circ}$ are adjacent and form a straight - line, we have the equation $5y+2y + 12=180$.
Combining like terms gives $7y+12 = 180$.
Subtract 12 from both sides: $7y=180 - 12=168$.
Divide both sides by 7: $y=\frac{168}{7}=24$.

Step2: Set up equation for x

The right - angle is 90 degrees, and the angle $(5x)^{\circ}$ and the right - angle are adjacent. So $5x=90$.
Divide both sides by 5: $x=\frac{90}{5}=18$.

Answer:

$x = 18$
$y = 24$