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Question

# In the given figure, ABCD is a parallelogram. From the given options, select the values of x and y.

A
x=45
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B
y=105
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C
y=30
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D
x=75
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Solution

## The correct option is C y=30∘ We know that the opposite angles of a parallelogram are equal. So, (3x−10)∘=(x+80)∘⇒3x−x=80∘+10∘⇒2x=90∘⇒x=45∘ Also, the consecutive angles of a parallelogram are supplementary. So, ∠B+∠C=180∘(3x−10)∘+(y+25)∘=180∘(3×45∘)−10∘+y+25∘=180∘135∘−10∘+y+25∘=180∘⇒125∘+y+25∘=180∘⇒y=180∘–125∘−25∘⇒y=30∘

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