Question

find the values of x and y.
2y + 30 = x
x =
y =

Explanation:

Step1: Use the property of a right - angled triangle

In a right - angled triangle, the exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles. Here, one non - adjacent interior angle is \(y\) and the other is \(90^{\circ}\). So \(x=y + 90\).

Step2: Substitute \(x\) in the given equation

We know that \(2y+30=x\). Substitute \(x=y + 90\) into \(2y+30=x\). Then \(2y+30=y + 90\).

Step3: Solve for \(y\)

Subtract \(y\) from both sides of the equation \(2y+30=y + 90\).
\(2y - y+30=y - y+90\), which gives \(y+30 = 90\).
Subtract 30 from both sides: \(y=90 - 30\), so \(y = 60\).

Step4: Solve for \(x\)

Substitute \(y = 60\) into \(x=y + 90\). Then \(x=60+90\), so \(x = 150\).

Answer:

\(x = 150\), \(y = 60\)