1. Introduction to Angles. Angle Pairs 1-3
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Holt Geometry

2. Warm Up 1. Draw AB and AC, where A, B, and C are noncollinear.
2. Draw opposite rays DE and DF.
Solve each equation.
3. 2x x – 4 + 3x – 5 = 180
4. 5x + 2 = 8x – 10 C B A
Possible answer: E F D 31 4

3. Objectives Name and classify angles.
Identify adjacent, vertical, complementary, and supplementary angles.
Find measures of pairs of angles.

4. Vocabulary angle right angle vertex obtuse angle
interior of an angle straight angle
exterior of an angle congruent angles
measure angle bisector
degree
acute angle

5. Vocabulary adjacent angles linear pair complementary angles
supplementary angles
vertical angles

6. An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number.

7. The set of all points between the sides of the angle is the interior of an angle. The exterior of an angle is the set of all points outside the angle.
Angle Name
R, SRT, TRS, or 1
You cannot name an angle just by its vertex if the point is the vertex of more than one angle. In this case, you must use all three points to name the angle, and the middle point is always the vertex.

8. The measure of an angle is usually given in degrees
The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is of a circle. When you use a protractor to measure angles, you are applying the following postulate.

9. You can use the Protractor Postulate to help you classify angles by their measure. The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond with on a protractor.
If OC corresponds with c and OD corresponds with d,
mDOC = |d – c| or |c – d|.

12. Congruent angles are angles that have the same measure
Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent.
The Angle Addition Postulate is very similar to the Segment Addition Postulate that you learned in the previous lesson.

14. An angle bisector is a ray that divides an angle into two congruent angles.
JK bisects LJM; thus LJK  KJM.

18. You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°.
You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

19. Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. Vertical angles are two nonadjacent angles formed by two intersecting lines. 1 and 3 are vertical angles, as are 2 and 4.

21. Are x and y complementary angles?

22. 1.Are angles x and y complementary angles?
a)x = 25, y = 75
b) x= 32 y =58
c) x = 41.4 y =48.6
2.If x and y are complementary angles, find the value of the missing variable.
a) x= y =
x = y= 58.3
3. If angles x and y are complementary angles and
x = a. Write angle y in terms of a.

23. Are these pairs of angles complementary angles?
Are these pairs of angles adjacent angles?

24. Are these pair of angles supplementary angles?1 2
Are these pair of angles linear pairs?
If m<1 = x, write m<2 in terms of x.