When two lines intersect they form two pairs of opposite angles,
A + C and B + D. Another word for opposite angles are vertical
Vertical angles are always congruent, which means that they are
Adjacent angles are angles that come out of the same vertex.
Adjacent angles share a common ray and do not overlap.
The size of the angle xzy in the picture above is the sum of the
angles A and B.
Two angles are said to be complementary when the sum of the two
angles is 90°.
Two angles are said to be supplementary when the sum of the two
angles is 180°.
If we have two parallel lines and have a third line that crosses
them as in the ficture below - the crossing line is called a
When a transversal intersects with two parallel lines eight
angles are produced.
The eight angles will together form four pairs of corresponding
angles. Angles 1 and 5 constitutes one of the pairs. Corresponding
angles are congruent. All angles that have the same position with
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 area between the parallel lines like
angle 2 and 8 above are called interior angles whereas the angles
that are on the outside of the two parallel lines like 1 and 6 are
called exterior angles.
Angles that are on the opposite sides of the transversal are
called alternate angles e.g. 1 + 8.
All angles that are either exterior angles, interior angles,
alternate angles or corresponding angles are all congruent.
The picture above shows two parallel lines with a transversal.
The angle 6 is 65°. Is there any other angle that also measures
6 and 8 are vertical angles and are thus congruent which means
angle 8 is also 65°.
6 and 2 are corresponding angles and are thus congruent which
means angle 2 is 65°.
6 and 4 are alternate exterior angles and thus congruent which
means angle 4 is 65°.
Video lesson: Find the measure of all the
angles in the figure