Question

question
find the value of x, y, and z in the parallelogram below.
answer
attempt 1 out of 2
x = □ y = □ z = □

Explanation:

Step1: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary. So, \((-x - 1)^{\circ}+59^{\circ}=180^{\circ}\)

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Step2: Use the property of opposite angles in a parallelogram

Opposite angles in a parallelogram are equal. So, \((3y - 6)^{\circ}=59^{\circ}\)

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Step3: Use the property of consecutive angles (another pair)

Consecutive angles are supplementary. \((2z + 5)^{\circ}+(3y - 6)^{\circ}=180^{\circ}\), since \(3y-6 = 59\), then \((2z + 5)+59=180\)

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Answer:

\(x=-122\), \(y = \frac{65}{3}\), \(z = 58\)