Basic Mathematics for College Students

720 Chapter 9 An Introduction to Geometry

Solution

a.It is helpful to draw a figure, as shown to the right. Let x

represent the measure of the complement of the 35°

angle. Since the angles are complementary, we have

The sum of the angles’ measures must

be 90°.

To isolate x,undo the addition of 35°

by subtracting 35° from both sides:

90°35°55°.

The complement of a 35° angle has measure 55°.

b.It is helpful to draw a figure, as shown on the

right. Let yrepresent the measure of the

supplement of the 105° angle. Since the angles

are supplementary, we have

The sum of the angles’

measures must be 180°.

To isolate y,undo the addition of 105° by subtracting

105° from both sides: 180°105°75°.

The supplement of a 105° angle has measure 75°.

y75°

y105°180°

x55°

x35°90°

35°

90°

x

180°

y 105°

1.right angle, obtuse angle, acute angle, straight angle 2.35° 3. a.100° b.30°

4. a.15° b.50° c.130° 5. a.40° b.130°

ANSWERS TO SELF CHECKS

VOCABULARY

Fill in the blanks.

1. Three undefined words in geometry are , ,
   and.


2. A line has two endpoints.


3. A divides a line segment into two parts of
   equal length.


4. A is the part of a line that begins at some point
   and continues forever in one direction.


5. An is formed by two rays with a common
   endpoint.


6. An angle is measured in.


7. A is used to measure angles.


8. The measure of an angle is less than 90°.


9. The measure of a angle is 90°.


10. The measure of an angle is greater than 90°
    but less than 180°.


11. The measure of a straight angle is.


12. When two segments have the same length, we say
    that they are.


13. angles have the same vertex, are side-by-
    side, and their interiors do not overlap.


14. When two lines intersect, pairs of nonadjacent angles
    are called angles.


15. When two angles have the same measure, we say that
    they are.


16. The word sumindicates the operation of.


17. The sum of two complementary angles is.


18. The sum of two angles is 180°.

CONCEPTS

19. a. Given two points (say,Mand N), how many
    different lines pass through these two points?
    b. Fill in the blank: In general, two different points
    determine exactly one.


20. Refer to the figure.
    a. Name in another way.
    b. Do and name the same ray?

N

M C

NM

¡

MN

¡

NM

¡

SECTION 9.1 STUDY SET