When two lines crossing they kind two bag of the opposite angles, A + C and also B + D. One more word for opposite angles space vertical angles.

You are watching: Complementary adjacent angles formed by two intersecting lines

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Vertical angles are constantly congruent, which method that they room equal.

Adjacent angles room angles the come the end of the same vertex. Adjacent angles share a typical ray and do no overlap.

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The dimension of the edge xzy in the photo above is the sum of the angle A and also B.

Two angles are claimed to it is in complementary when the sum of the two angles is 90°.

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Two angle are claimed to it is in supplementary when the amount of the two angles is 180°.

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If we have two parallel lines and have a third line that crosses them as in the ficture below - the crossing line is referred to as a transversal

When a transversal intersects with two parallel currently eight angles room produced.

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The eight angles will certainly together type four pairs of equivalent angles. Angle 1 and also 5 constitutes among the pairs. Corresponding angles space congruent. All angle that have the same place with regards to the parallel lines and the transversal are equivalent pairs e.g. 3 + 7, 4 + 8 and 2 + 6.

Angles that are in the area between the parallel lines choose angle 2 and 8 over are dubbed interior angles whereas the angles that are on the exterior of the two parallel lines like 1 and also 6 are referred to as exterior angles.

Angles that are on the opposite sides of the transversal room called alternate angles e.g. 1 + 8.

All angles that room either exterior angles, inner angles, alternating angles or corresponding angles space all congruent.

Example

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The picture above mirrors two parallel lines through a transversal. The angle 6 is 65°. Is there any kind of other angle that additionally measures 65°?

6 and 8 space vertical angles and are for this reason congruent which way angle 8 is also 65°.

6 and 2 are corresponding angles and are thus congruent which means angle 2 is 65°.

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6 and 4 are alternate exterior angles and also thus congruent which means angle 4 is 65°.