In the given figure, AB is parallel to EF. ED is parallel to CB and angle APE is 60 degrees.
What is the value (in degrees) of angle EQC?
Given:
AB ∥ EF
ED ∥ CB
∠APE = 60°
Find ∠EQC
Concept Used:
Corresponding angles between parallel lines
Vertically opposite angles
Formula Used:
Angles formed by parallel lines are equal.
Solution:
At point P, ∠APE = 60°.
Since AB ∥ EF and ED ∥ CB, the angle formed between EF and CB at Q will be equal to the angle formed between AB and ED at P.
Thus, the acute angle at Q is also 60°.
∠EQC is vertically opposite to this acute angle, so:
∠EQC = 60°
Therefore,
∠EQC = 60°
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