Question

10 the diagram below shows an isosceles trapezoid: diagram of isosceles trapezoid with angles x°, y°, 72°, z° and marked congruent legs x = blank degrees. y = blank degrees. z = blank degrees.

Explanation:

Step1: Use the property of adjacent angles in a trapezoid

In a trapezoid, adjacent angles along the non - parallel sides are supplementary (sum to \(180^{\circ}\)).
For angle \(x\) and the \(72^{\circ}\) angle: \(x + 72^{\circ}=180^{\circ}\)
\(x=180^{\circ}-72^{\circ}\)
\(x = 108^{\circ}\)

Step2: Use the property of an isosceles trapezoid

In an isosceles trapezoid, base angles are equal.
Since the trapezoid is isosceles, \(z = 72^{\circ}\)

Step3: Use the property of adjacent angles in a trapezoid again

For angle \(y\) and angle \(z\): \(y+z = 180^{\circ}\)
Since \(z = 72^{\circ}\), then \(y=180^{\circ}-72^{\circ}\)
\(y = 108^{\circ}\)

Answer:

\(x = 108\) degrees.
\(y = 108\) degrees.
\(z = 72\) degrees.