OBJECTIVE 3 Solve problems about angles.An important result of Euclidean
geometry (the geometry of the Greek mathematician Euclid) is thatthe sum of the
angle measures of any triangle is180°.This property is used in the next example.
Finding Angle MeasuresFind the value of x, and determine the measure of each angle in FIGURE 8.
Step 1 Readthe problem. We are asked to find the measure of each angle.
Step 2 Assign a variable.
Let the measure of one angle.
Step 3 Write an equation.The sum of the three measures
shown in the figure must be 180°.
Step 4 Solve. Combine like terms.
Subtract 230.
Multiply byStep 5 State the answer.One angle measures 50°. The other two angles measure
and
Step 6 Check.Since the answers are correct.
NOW TRY50° +70°+ 60°= 180°,
210 - 3 x= 210 - 31502 = 60°.
x+ 20 = 50 + 20 =70°
x= 50 - 1.
- x=- 50
- x+ 230 = 180
x+ 1 x+ 202 + 1210 - 3 x 2 = 180
x=
EXAMPLE 4
84 CHAPTER 2 Linear Equations, Inequalities, and Applications
In Example 3,it was easier to let the variable represent a quantity other than the
one that we were asked to find. It takes practice to learn when this approach
works best.
PROBLEM-SOLVING HINT
x° (210 – 3x)°(x + 20)°FIGURE 8Complete solution available
on the Video Resources on DVD
2.4 EXERCISES
Concept Check Solve each problem.
1.What amount of money is found in a coin hoard containing 14 dimes and 16 quarters?
2.The distance between Cape Town, South Africa, and Miami is 7700 mi. If a jet averages
550 mph between the two cities, what is its travel time in hours?
3.Tri Phong traveled from Chicago to Des Moines, a distance of 300 mi, in 10 hr. What was
his rate in miles per hour?
4.A square has perimeter 80 in. What would be the perimeter of an equilateral triangle
whose sides each measure the same length as the side of the square?Concept Check Answer the questions in Exercises 5– 8.
5.Read over Example 3in this section. The solution of the equation is 10. Why is 10 mph
not the answer to the problem?NOW TRY
EXERCISE 4
Find the value of x, and
determine the measure of
each angle.
NOW TRY ANSWER
- 41°, 52°, 87°
x°
(x + 11)°(3x – 36)°