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Example 1 of Angles Pairs and Parallel Lines

Question:

In the figure below, line AB parallel to line CD, intersected by line EF at point G and H respectively. If angle CHF is 30 degree, what is the value of x in degree?

Solution:

Since line segments CD and EF intersect at point H, so angle GHD = angle CHF = 30^o. (Vertical angles are congruent)

Since AB // CD (Given), so angle EGB = angle GHD = 30 degrees (Corresponding angles are congruent)

x = angle EGB = 30^o.

The value of x is 30^o.