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We used the properties of corresponding and alternate Measuring Angles formed when a transversal cuts parallel lines to find the measures of the requested angles. These yields ∠FCD = ∠ABE = 64° and ∠BCD = 116°.
First of all, we use the concept of corresponding angles which arise when a transversal cuts two parallel lines, stating that they have the same measure. Since lines AB and CD are parallel and angles ABC and FCD are corresponding, we have ∠FCD = 64°.
Next, we identify that angles ABC and BCD form a straight line. They are supplementary and add up to 180°. Therefore, the measure of ∠BCD = 180° - ∠ABC = 116°.
Finally, we use the concept of alternate angles to determine the measure of ∠ABE. Since AB is parallel to CD and BC is a transversal, ∠ABC and ∠ABE are alternate angles and thus have the same measure. Therefore, we can conclude that ∠ABE = 64°.
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The probable question may be:
Parallel lines are cut by the transversal shown. Determine the measures of the requested angles.
In the figure, line AB parallel to line CD and angle ABC=64 degree. There is a line FE which has B and C points on it. Determine the measures of angles ABE. FCD and BCD.
