When 2 lines intersect they develop two pairs of opposite angles, A + C and also B + D. Anvarious other word for opposite angles are vertical angles.

You are watching: Opposite angles formed by two intersecting lines

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Vertical angles are constantly congruent, which means that they are equal.

Adjacent angles are angles that come out of the exact same vertex. Adjacent angles share a prevalent ray and also do not overlap.

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The size of the angle xzy in the photo over is the sum of the angles A and also B.

Two angles are shelp to be complementary when the sum of the two angles is 90°.

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Two angles are sassist to be supplementary when the sum of the two angles is 180°.

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If we have two parallel lines and also have actually a 3rd line that crosses them as in the ficture below - the crossing line is dubbed a transversal

When a transversal intersects with 2 parallel lines eight angles are created.

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The eight angles will together form four pairs of matching angles. Angles 1 and 5 constitutes among the pairs. Corresponding angles are congruent. All angles that have the same position via regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.

Angles that are in the location between the parallel lines choose angle 2 and also 8 above are called interior angles whereas the angles that are on the external of the two parallel lines prefer 1 and also 6 are called exterior angles.

Angles that are on the opposite sides of the transversal are dubbed different angles e.g. 1 + 8.

All angles that are either exterior angles, interior angles, alternative angles or equivalent angles are all congruent.

Example

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The picture above reflects 2 parallel lines via a transversal. The angle 6 is 65°. Is there any kind of other angle that additionally measures 65°?

6 and also 8 are vertical angles and are therefore congruent which suggests angle 8 is likewise 65°.

6 and 2 are corresponding angles and also are for this reason congruent which suggests 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°.