[geometry word problems][section 12]
(1.) The measures of the angles of a
triangle can be
represented by s, (1/2)s, and
3s. Find the measure
of each angle of the triangle.
s + (1/2)s + 3s = 180 here is the problem
4.5s = 180 combine like terms
____ ____
4.5 4.5 divide each side by 4.5
s = 40 divide and cancel
(1/2)s here is the problem
= (1/2)(40) replace s with 40
= 20 multiply
3s here is the problem
= 3(40) replace s with 40
= 120 multiply
results: The angles are 40, 20, and 120.
(2.) The measure of one angle of a
triangle is 70o . The
measure of each of the other
angles can be represented
by 5x. Find the measures of the two angles.
70 +
5x + 5x = 180 here is the problem
10x + 70 = 180 combine like terms
-70 -70
subtract 70 from each side
____________________
10x = 110 subtract
____ ____
10 10 divide each side by 10
x = 11 divide and cancel
5x here is the problem
= 5(11) replace x with 11
= 55 multiply
results: The angles are 70, 55 and 55.
(3.) The measure of one angle of a
triangle can be represented
by 10p. The measure of each of the other two angles
is
15 more than the first angle. Find the measure of each
angle of the triangle.
10p
+ (10p + 15) + (10p + 15) = 180 here is
the problem
30p + 30 = 180 combine like terms
-30 -30
subtract 30 from each side
____________________
30p = 150 subtract
____ ____
30
30 divide each side by 30
p = 5 divide and cancel
10p here is the problem
= 10(5) replace p with 5
= 50 multiply
10p + 15 here is the problem
= 10(5) + 15 replace p with 5
= 65 multiply & add
results: The angles are 50, 65, and 65 .
(4.) The sum of the measures of two
angles is 90o . The
measure of one of these angles is 2r; the measure of
the other angle is 2r - 18. Find the measure of each
of these angles.
2r + 2r - 18 = 90 here is the problem
4r - 18 = 90 combine like terms
+18 +18
add 18 to each side
_______________
4r =
108 add
___ ____
4 4
divide each side by 4
r = 27 divide and cancel
2r here is the problem
= 2(27) replace r with 27
= 54 multiply
2r - 18 here is the problem
= 2(27) - 18 replace r with 27
= 36 multiply and subtract
results: the angles are 54 and 36.
(5.) The sum two angles is 90o
. The measures of the angles
can be represented by x and (x +
28). Find the measure
of each angle.
x + x + 28 = 90 here is the problem
2x + 28 = 90 combine like terms
-28 -28
subtract 28 from each side
________________
2x = 62 subtract
___ ____
2 2 divide each side by 2
x = 31 divide and cancel
x + 28 here is the problem
= 31 + 28 replace x with 31
= 59 add
results: the angles are 31 and 59.
(6.) The sum of two angles is 90o
. The measures of the
angles can be represented by t
and (t - 12). Find the
measure of each angle.
t +
t - 12 = 90 here is the
problem
2t - 12 = 90 combine like terms
+ 12 +12
add 12 to each side
_______________
2t = 102 add
__ ____
2 2 divide each side by 2
t = 51 divide and cancel
t - 12 here is the problem
= 51 - 12 replace t with 51
= 39 subtract
results: the angles are 51 and 39.
(7.) The sum of two angles is 180o
. Their measures can
be represented by y and (y +
36). Find the measure of
each angle.
y + y + 36 = 180 here is the problem
2y + 36 = 180 combine like terms
-36 -36
subtract 36 from each side
__________________
2y
= 144 subtract
___ _____
2 2
divide each side by 2
y = 72 divide and cancel
y + 36 here is the problem
= 72 + 36 replace y with 72
= 108 add
results: the angles are 72 and 108.
(8.) The sum of two angles is 180o
. Their measures can be
represented by w and (3w +
18). Find the measure of
each angle.
w +
3w + 18 = 180 here is the
problem
4w + 18 = 180 combine like terms
-18 -18
subtract 18 from each side
_________________
4w =
162 subtract
__ ______
4 4 divide each side by 4
w = 40.5 divide and cancel
3w + 18 here is the problem
= 3(40.5) + 18 replace w with 40.5
= 121.5 + 18 multiply
= 139.5 add
results: the angles are 40.5 and 139.5
(9.) The measures of the angles of a
parallelogram can by
represented by x, x, 3x, and
3x. Find the measure of
each angle of the parallelogram.
x + x + 3x + 3x = 360 here is the problem
8x = 360 combine like terms
___ ___
8 8
divide each side by 8
x = 45 divide and cancel
3x here is the problem
= 3(45) replace x with 45
= 135 multiply
results: the angles are 45, 45, 135, and
135
(10.) The sum of the measures of two
angles is 180o . The
measure of one angle is 5x. The measure of the other
angle is twice the first. Find the measure of each
angle.
5x + 2(5x) = 180 here is the problem
5x + 10x = 180 multiply
15x = 180 combine like terms
_____ _____
15 15 divide each side by 15
x = 12 divide and cancel
5x here is the problem
= 5(12) replace x with 12
= 60 multiply
results:
the angles are 60 and 120
(11.) The sum of the measures of two
angles is 90o . The
measure of one angle is 4q. The measure of the second
angle is three times the
first. Find the measure of
each angle.
4q + 3(4q) = 90 here is the
problem
4q + 12q = 90 multiply
16q = 90 combine like terms
____ ___
16 16
divide each side by 16
q = 5.625 divide and cancel
4q here is the problem
= 4(5.625) replace q with 5.625
= 22.5 multiply
3(22.5) here is the problem
= 67.5 multiply
results: the angles are 22.5 and 67.5
(12.) The sum of the measures of two
angles is 180o . The
measure of one angle is 7t. The measure of the second
angles is 2 more than the
first. Find the measure of
each angle.
7t + 7t + 2 = 180 here is the problem
14t + 2 = 180 combine like terms
-2 -2
subtract 2 from each side
__________________
14t = 178 subtract
____ ____
14 14 divide each side by 14
t = 89/7 reduce and cancel
7t here is the problem
= 7(89/7) replace t with 89/7
= 89 cancel
results: the angles are 89 and 91 .