Inna Buff, Sabrina Lowrie, and Lisa Mann

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is the union of two rays having the same endpoint. The endpoint is called theanglevertexof the angle. The rays are called thesidesof the angle. The size of an angle is measured indegrees, denoted by this symbol: x°Objects of the same shape and size are said to be

.congruentAngles are congruent if they have the same degree measure.

An L-shaped angle is called a

. A right angle will always measureright angle90°.Therefore, all right angles are congruent. Lines that intersect to form right angles are said to beperpendicular. In other words,perpendicular lines form right angles.

An angle whose sides form a straight line is called a

and has a measure ofstraight angle180°.

An

is an angle whose measure isacute anglebetween 0° and 90°.

An

is an angle whose measure isobtuse anglebetween 90° and 180°.

Many special relationships exist between pairs of angles.

Let's take a look at them . . .

Two angles are

if they have the same vertex and share a common side, but do not overlap or have any points in common.adjacent

Two angles are

if the sum of their measures is 90°. When this occurs, either angle is called thecomplementarycomplementof the other. Complementary angles are not necessarily adjacent.

When two angles are

adjacent and complementary, do you know what type of angle is formed by their exterior sides??

Two angles are

if the sum of their measures is 180°. When this occurs, either angle is called thesupplementarysupplementof the other. Supplementary angles are not necessarily adjacent.

When two angles are

adjacent and supplementary, do you know what type of angle is formed by their exterior sides??

When two lines intersect, they always form four angles with a common vertex. Each pair of angles which are not adjacent (and therefore opposite) are called

and are equal in measure.vertical angles

How about this for a new angle . . .

Let's try some Practice Problems !

- If two angles are supplementary, find the measure of the smaller angle if the measures of the two angles are in the ratio of: a) 1 : 8 b) 3 : 5
- If two angles are complementary, find the measure of the smaller angle if the measures of the two angles are in the ratio of: a) 2 : 3 b) 3 : 1
- The measure of the supplement of an angle is three times as great as the measure of the complement of the same angle. What is the measure of the angle?
- The difference between the measures of an angle and its complement is 14. Find the measure of the smaller of the two angles.
- The difference between the measures of an angle and its supplement is 22. Find the measure of the smaller of the two angles.
If you've mastered Angles, you'll do great with Triangles!

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Science Education Program/Comments