Question

what are the values of x and y?
w
x
u
54°
v
y
x =
°
y =
°

Explanation:

Step1: Identify the triangle type

The triangle has two equal - length sides (marked with the red tick marks), so it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. The side opposite angle \(U\) (which is \(54^{\circ}\)) and the side opposite angle \(x\) are equal? Wait, no. Wait, the sides \(WV\) and \(WU\) (wait, no, looking at the triangle, the two equal - length sides: one is on \(WU\) and one is on \(WV\). So the angles opposite them: angle \(V\) (angle \(y\)) and angle \(U\) (angle \(54^{\circ}\))? Wait, no, let's re - examine. In triangle \(WVU\), the two equal sides are \(WV\) and \(WU\)? Wait, the tick marks: one on \(WU\) and one on \(WV\). So the angles opposite these sides: angle \(V\) (opposite \(WU\)) and angle \(U\) (opposite \(WV\)) are equal. Wait, angle \(U = 54^{\circ}\), so angle \(y=\angle U = 54^{\circ}\) because they are opposite equal sides.

Step2: Calculate angle \(x\)

The sum of the interior angles of a triangle is \(180^{\circ}\). So we know that the sum of angles in triangle \(WVU\) is \(x + y+54^{\circ}=180^{\circ}\). We already found that \(y = 54^{\circ}\), so substitute \(y\) into the equation: \(x+54^{\circ}+54^{\circ}=180^{\circ}\). Then \(x=180^{\circ}- 54^{\circ}-54^{\circ}\). Calculate \(180 - 54 - 54=72\). So \(x = 72^{\circ}\) and \(y = 54^{\circ}\).

Answer:

\(x = 72\), \(y = 54\)