Question

Find the measure of each angle in Triangle ABC. m∠a=(40x−21)°m∠b=(31−2x)°m∠c=(x+14)°

m
∠
a
=
(
40
x
−
21
)
°
m
∠
b
=
(
31
−
2
x
)
°
m
∠
c
=
(
x
+
14
)
°
A. m∠a=23°m∠b=139°m∠c=18°
m
∠
a
=
23
°
m
∠
b
=
139
°
m
∠
c
=
18
°
B. m∠a=181°m∠b=39°m∠c=10°
m
∠
a
=
181
°
m
∠
b
=
39
°
m
∠
c
=
10
°
C. m∠a=18°m∠b=41°m∠c=121°
m
∠
a
=
18
°
m
∠
b
=
41
°
m
∠
c
=
121
°
D. m∠a=139°m∠b=23°m∠c=18°

Answer 1

D. m∠a=139°, m∠b=23°, m∠c=18°

Explanation:

This is a multiple-choice question that can be answered simply by considering the reasonableness of the answers.

__

The expression for ∠a suggests it will be by far the largest of the angles, eliminating choices A and C.

No angle in a triangle is more than 180°, eliminating choice B.

The expression for ∠b suggests it will have a measure less than 31°. This confirms choice D as the correct one.

m∠a=139°, m∠b=23°, m∠c=18°

__

If you want to work the problem, you use the fact that the sum of angles is 180°

∠a +∠b +∠c = 180°

(40x -21)° +(31 -2x)° +(x +14)° = 180°

39x +24 = 180 . . . . . . . . . divide by °, collect terms

39x = 156 . . . . . . . . . . subtract 24

x = 4 . . . . . . . . . . . divide by 39

Then the measures of the angles are ...

∠a = (40×4 -21)° = 139°

∠b = (31 -2×4)° = 23°

∠c = (4 +14)° = 18°