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