Question - Finding the Values of Angles in a Geometric Figure

Solution:

Given that line AB is parallel to line CD, angle AEB = angle DEC as corresponding angles.

Angle DEC = 70° (given).

Therefore, angle AEB = 70°.

Angle DEB = angle BEA as alternate interior angles, hence angle DEB = 28°.

In triangle DEB, sum of angles = 180°.

Therefore, angle EDB = 180° - 70° - 28° = 82°.

Since angle EDB = angle EAB as alternate interior angles and line AB is parallel to line CD, angle EAB = 82° as well.

In triangle AEB, sum of angles = 180°.

Therefore, angle A = 180° - 70° - 82° = 28°.

Hence, x = 28° and y = 82°.

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