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Example Question #522 : Plane Geometry
If ,
, and
, what is the measure, in degrees, of
?
Possible Answers:
62
148
58
122
32
Correct answer:
148
Explanation:
The question states that . The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent; therefore, we know the following measure:
The sum of angles of a triangle is equal to 180 degrees. The question states that ; therefore we know the following measure:
Use this information to solve for the missing angle:
The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:
The measure of is 148 degrees.
Hugues
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