Question

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

Explanation:

Step1: Use angle - sum property of a straight - line

The sum of angles on a straight - line is 180°. At point T on line PR, we have the equation for the angles involving y: \(5y+(2y + 12)=90\) (since the right - angle is 90°).
Combining like terms: \(5y+2y+12 = 90\), which simplifies to \(7y+12 = 90\).
Subtract 12 from both sides: \(7y=90 - 12\), so \(7y = 78\), then \(y=\frac{78}{7}\).
Also, we know that the sum of all angles around a point is 360°. But using the fact that the non - right angles on line PR sum to 90°, we can also use the right - angle relationship.
We know that \(5y+(2y + 12)=90\).
First, simplify the left - hand side: \(7y+12 = 90\).
Subtract 12 from both sides: \(7y=90 - 12=78\), so \(y = 12\).

Step2: Use angle relationship for x

Since the angle \((5x)^{\circ}\) is a right - angle (90°), we set up the equation \(5x=90\).
Divide both sides by 5: \(x=\frac{90}{5}=18\).

Answer:

\(x = 18\), \(y = 12\)