Two angles whose sum is 180° are called supplementary angles. The measure of ∠AGE in the given figure is 129°.
What are supplementary angles?
Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
In the given figure, line segment CE is a straight line. Therefore, the sum of the angles formed on the same side of the line will be a linear pair.
Thus, the measure of the angles can be rewritten as,
∠AGC + ∠AGE = 180°
51° + ∠AGE = 180°
∠AGE = 180° - 51°
∠AGE = 129°
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