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How much do corresponding angles add up to?

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Last updated date: 13th Jun 2024
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Answer
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Hint:Corresponding angles are those angles which are formed when two lines are crossed by another line (which is known as transversal). The angles which are created in the matching corners at each intersection are known as corresponding angles. Like corresponding angles, we can have both alternate interior angles and alternate exterior angles. Here, in this question we have to find out how much do corresponding angles add up to.

Complete step by step solution:
We know that corresponding angles are formed when two parallel lines are intersected by a transversal. Following is a diagram of corresponding angles:
Here, two lines are parallel and are intersected by transversal and dividing each intersection into four angles.$\angle A$ and $ \angle E$,$ \angle B$ and $\angle F$,$ \angle C$ and $\angle G$,$ \angle D$ and $\angle H$ are pairs of corresponding angles.
The corresponding angles theorem says, ‘’if a line intersects two parallel lines, then the
corresponding angles in the two intersection regions are congruent’’. So, we can say that the angles which are formed by corresponding angles are congruent.
On the basis of their sum, corresponding angles can be:
1. Supplementary corresponding angles (if sum is $180$ degrees)
2. Complementary corresponding angles (if sum is $90$ degrees)

Note: Students should note that a pair of corresponding angles always lie on the same side of transversal. Corresponding angles can form into supplementary angles if the transversal intersects perpendicularly two parallel lines. Students should keep in mind that not all the corresponding angles are equal. Corresponding angles are equal only when the transversal intersects two parallel
lines.