Pairs of Angles

1. Pairs of Angles

2. S vertex T Angles – sides and vertex angle This figure is called an _____. Some parts of angles have special names. The common endpoint is called the ______, side vertex and the two rays that make up the sides of the angle are called the sides of the angle. side R

3. S vertex SRT R TRS 1 T Naming Angles There are several ways to name this angle. 1) Use the vertex and a point from each side. or side The vertex letter is always in the middle. 2) Use the vertex only. 1 R side If there is only one angle at a vertex, then theangle can be named with that vertex. 3) Use a number.

4. Angles Review C A 1 B ABC 1 B CBA BA and BC 1) Name the angle in four ways. 2) Identify the vertex and sides of this angle. vertex: Point B sides:

5. A A A Angle Classification Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle. obtuse angle Greater than 90° right angle Equal to 90 ° acute angle Less than 90 °

6. 40° 110° 90° 50° 75° 130° Angle Classification Classify each angle as acute, obtuse, or right. Acute Obtuse Right Obtuse Acute Acute

7. Z Y XY and XZ are ____________. X Straight Angles Opposite rays ___________ are two rays that are part of the same line and have only their endpoints in common. opposite rays The figure formed by opposite rays is also referred to as a ____________. A straight angle measures 180 degrees. straight angle

8. A B D C Adjacent Angles When you “split” an angle, you create two angles. The two angles are called _____________ adjacent angles 2 adjacent = next to, joining. 1 1 and 2 are examples of adjacent angles. They share a common ray. Name the ray that 1 and 2 have in common.

9. B 2 1 1 2 G N L 1 J 2 Adjacent Angles Determine whether 1 and 2 are adjacent angles. No. They have a common vertex B, but _____________ no common side Yes. They have the same vertex G and a common side with no interior points in common. No. They do not have a common vertex or ____________ a common side The side of 1 is The side of 2 is

10. E D A 60° F 30° B C Complementary Angles Two angles are complementaryif and only if The sum of their degree measure is90. mABC + mDEF= 30 + 60 = 90

11. I 75° 15° H P Q 40° 50° H S U V 60° T 30° Z W Complementary Angles Some examples of complementary angles are shown below. mH + mI = 90 mPHQ + mQHS = 90 mTZU + mVZW = 90

12. D C 130° 50° E B F A Supplementary Angles If the sum of the measure of two angles is 180, they form a special pair of angles called supplementary angles. Two angles are supplementary if and only if the sum of their degree measure is 180. mABC + mDEF= 50 + 130 = 180

13. I 75° 105° H Q 130° 50° H S P U V 60° 120° 60° Z W T Supplementary Angles Examples of supplementary angles are shown below. mH + mI = 180 mPHQ + mQHS = 180 mTZU + mUZV = 180 and mTZU + mVZW = 180

14. Vertical Angles When two lines intersect, ____ angles are formed. four There are two pair of nonadjacent angles. These pairs are called _____________. vertical angles 1 4 2 3

15. Vertical Angles Two angles are verticalif and only if they are two nonadjacent angles formed by a pair of intersecting lines. Vertical angles: 1 and 3 1 4 2 2 and 4 3

16. Vertical Angles Vertical angles are congruent. n m 2 1  3 3 1 2  4 4

17. 130° x° Vertical Angles Find the value of x in the figure: The angles are vertical angles. So, the value of x is 130°.