SECTION 2.5 Formulas and Additional Applications from Geometry^123
Finding Angle MeasuresRefer to the appropriate figure in each part.
(a) Find the measure of each marked angle in FIGURE 13.
Since the marked angles are vertical angles, they have equal measures.
Set equal to.
Subtract 4x.
Add 5.
Divide by 2.Replace xwith 12 in the expression for the measure of each angle.
Each angle measures 67°.
6 x- 5 = 61122 - 5 = 72 - 5 = 67
4 x+ 19 = 41122 + 19 = 48 + 19 = 67
12 =x
24 = 2 x
19 = 2 x- 5
4 x+ 19 = 6 x- 5 4 x+ 19 6 x- 5
NOW TRY EXAMPLE 5
EXERCISE 5
Find the measure of each
marked angle in the figure.
(6x + 2)° (8x – 8)°(4x + 19)° (6x – 5)°FIGURE 13(3x – 30)° (4x)°FIGURE 14The angles have equal
measures, as required.This is not
the answer.(b) Find the measure of each marked angle in FIGURE 14.
The measures of the marked angles must add to 180° because together they
form a straight angle. (They are also supplementsof each other.)
Combine like terms.
Add 30.x= 30 Divide by 7.
7 x= 210
7 x- 30 = 180
13 x- 302 + 4 x= 180
Replace xwith 30 in the expression for the measure of each angle.
The two angle measures are 60°and 120°. NOW TRY
4 x= 41302 = 120
3 x- 30 = 31302 - 30 = 90 - 30 = 60
Don’t
stop here!The measures of the angles
add to 180º, as required.CAUTION In Example 5,the answer is notthe value of x. Remember to sub-
stitute the value of the variable into the expression given for each angle.
OBJECTIVE 4 Solve a formula for a specified variable. Sometimes we want
to rewrite a formula in terms of a different variable in the formula. For example,
consider the formula for the area of a rectangle.
How can we rewrite in terms of W?
The process whereby we do this is called solving for a specified variable,or solving
a literal equation.
a=LW
a= LW,
NOW TRY ANSWER
- 32°, 32°