What is the X angle called?

When two lines are crossed by another line (called the Transversal):

The angles in matching corners are called Corresponding Angles.

In this example, these are corresponding angles:

• a and e
• b and f
• c and g
• d and h

Parallel Lines

When the two lines being crossed are Parallel Lines the Corresponding Angles are equal.

(Click on "Corresponding Angles" to have them highlighted for you.)

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles.

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

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 transversal

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.

Example

The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65°?

You've certainly used the word "angle" in common life, but it also has an important meaning in mathematics. One subject you'll want to be familiar with is the different types, or classifications, of angles, determined by the measure of the angle. This page is a simple, easy-to-follow beginner's guide to the different types of angles.

Three Main Types of Angles

Acute - any angle which measures less than 90 degrees. These angles appear "sharp," like the blade on a knife.

Example: The angle ABC measures 40 degrees. Angle ABC is acute.

Right - any angle which measures exactly 90 degrees. These are like the edges of a wooden block.

Sample: The angle CAT measures 90 degrees. The angle CAT is a right angle.

Obtuse - any angle which measures more than 90 degrees but less than 180 degrees. These are "fat" angles that are very wide.

Sample: angle DEF measures 125 degrees. Then angle DEF is obtuse.

Special Case

Straight - any angle which measures exactly 180 degrees. This isn't even really an angle... it's just a straight line!

Sample: Points ABC lie on line L forming a STRAIGHT LINE. Then line L is a straight line.

Relationships between several angles

Vertical Angles - Two angles formed by intersecting lines. They can not be adjacent but are always equal in measure. They are across from one another in the corners of the "X" formed by the lines.

In the above picture, angles 1 and 3 and angles 2 and 4 are vertical because they are across from each other. Now, angles 1 and 2 and angles 3 and 4 are NOT vertical angles.

Complementary Angles - Two angles whose measures add up to 90 degrees.

Sample: angle A = 30 degrees and and angle B = 60 degrees.
Then angle A + angle B = 90 degrees. We can say angles A and B are complementary.

Supplementary Angles - Two angles whose measures add up to 180 degrees. Supplementary angles can be placed so that they form a straight line.

Sample: angle A = 80 degrees and angle B = 100 degrees. Then angle A + angle B = 180 degrees. We can say that angles A and B are supplementary.

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