Page 655 - Basic College Mathematics with Early Integers

632 C HAPTE R 9 I GEOMETRY

The sum of the measures of the angles of a triangle is 180°.

x
y z
mx+my+mz=180

PRACTICE 1 Example 1 Find the measure of ∠a.
Find the measure of ∠x.
a

25 95
35

Solution: Since the sum of the measures of the three angles is 180°, we have
110
x measure of ∠a, or m ∠a, = 180° - 95° - 35° = 50°
To check, see that 95° + 35° + 50° = 180°.
Work Practice 1

We can classify triangles according to the lengths of their sides. (We will use tick
marks to denote the sides and angles of a figure that are equal.)

Equilateral triangle Isosceles triangle Scalene triangle
All three sides are Two sides are the No sides are the
the same length. Also, same length. Also, same length. No
all three angles have the angles opposite angles have the
the same measure. the equal sides same measure.
have equal measure.

One other important type of triangle is a right triangle. A right triangle is a
triangle with a right angle.The side opposite the right angle is called the hypotenuse,
and the other two sides are called legs.

hypotenuse
leg

leg
PRACTICE 2 Example 2 Find the measure of ∠b.
Find the measure of ∠y.
b

25
30
Solution: We know that the measure of the right angle, , is 90°. Since the sum

y
of the measures of the angles is 180°, we have Copyright 2012 Pearson Education, Inc.
measure of ∠b, or m ∠b, = 180° - 90° - 30° = 60°
Answers
1. 45° 2. 65° Work Practice 2