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Question

# In the given figure, line PQ and line MN intersect at O. Determine the value of y when x=60°. Further, determine the value of x when y=40°.

A
y=60° and x=70°
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B
y=70° and x=60°
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C
y=50° and x=80°
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D
y=80° and x=50°
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Solution

## The correct option is A y=60° and x=70°From the given figure, ∠POM and ∠MOQ form a linear pair of angles. ⇒2x+y=180∘ Case (1) : When x=60∘ 2×60∘+y=180∘ ⇒y=180∘−120∘=60∘ Case (2) : When y=40∘ 2x+40∘=180∘ ⇒2x=180∘−40∘=140∘ ⇒x=70∘ ∴ When x=60∘, y=60∘ and when y=40∘, x=70∘.

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