Question

find the values of x and y.
(3x)°
(8y - 9)°
x = 15
y =

Explanation:

Step1: Use angle - sum property for right - angle

The sum of angles forming a right - angle is 90°. So, \(3x + x+30 = 90\).
Combining like terms, we get \(4x+30 = 90\).
Subtract 30 from both sides: \(4x=90 - 30\), so \(4x = 60\).
Divide both sides by 4: \(x=\frac{60}{4}=15\) (which is already given).

Step2: Use angle - sum property for straight - angle

The sum of angles on a straight - line is 180°. The right - angle is 90°, so the sum of the other two non - right angles \((8y - 9)+(3x)\) is 90°.
Since \(x = 15\), then \(3x=3\times15 = 45\).
We have the equation \((8y - 9)+45=90\).
First, simplify the left - hand side: \(8y+36 = 90\).
Subtract 36 from both sides: \(8y=90 - 36\), so \(8y = 54\).
Divide both sides by 8: \(y=\frac{54}{8}=\frac{27}{4}=6.75\).

Answer:

\(y = 6.75\)