Question

4.7 assignment
find the values of x and y.

x=

y=

Explanation:

Step1: Find \(x\)

Since the triangle has two equal sides (marked with the same tick), the angles opposite those sides are equal. So \(3x + 8=53\).
Subtract \(8\) from both sides: \(3x=53 - 8\), so \(3x = 45\).
Divide both sides by \(3\): \(x=\frac{45}{3}=15\).

Step2: Find \(y\)

The sum of angles in a triangle is \(180^{\circ}\).
We know two angles (\(53^{\circ}\) and \(53^{\circ}\)), so the third angle \((8y + 10)^{\circ}=180-(53 + 53)\).
Calculate \(180-(53 + 53)=180 - 106=74\).
So \(8y+10 = 74\).
Subtract \(10\) from both sides: \(8y=74 - 10\), so \(8y = 64\).
Divide both sides by \(8\): \(y=\frac{64}{8}=8\).

Answer:

\(x = 15\), \(y = 8\)