Question

in parallelogram lmno, what are the values of x and y?
(3x - 55)°
(2x)°
(5y)°
x = 11, y = 14
x = 11, y = 25
x = 55, y = 14
x = 55, y = 25

Explanation:

Step1: Use the property of consecutive angles in a parallelogram

In a parallelogram, consecutive angles are supplementary. So, \(2x+(3x - 55)=180\).

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(Wait, this is wrong. Actually, in a parallelogram, opposite angles are equal. \(\angle O=\angle M\), so \(2x=3x - 55\))

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Step2: Use the property of opposite angles

Also, \(\angle L=\angle N\) (opposite angles in a parallelogram). Since \(\angle L = 2x\), when \(x = 55\), \(\angle L=110^{\circ}\). And \(\angle N=(5y)^{\circ}\). Also, consecutive angles: \(\angle O+\angle N=180^{\circ}\), \(\angle O = 2x=110^{\circ}\), so \(110 + 5y=180\)

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Answer:

\(x = 55,y = 14\) (the third option \(x = 55,y = 14\))