Answer:
m<A = 139°; m<B = 23°; m<C = 18°
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180 deg.
Add the three measures and set the sum equal to 180. Then solve the equation for x. Then use the value of x to find each measure.
m<A + m<B + m<C = 180
(40x - 21) + (31 - 2x) + (x + 14) = 180
Drop all parentheses since they are not necessary.
40x - 21 + 31 - 2x + x + 14 = 180
Combine like terms on the left side.
40x - 2x + x - 21 + 31 + 14 = 180
39x + 24 = 180
Subtract 24 from both sides.
39x = 156
Divide both sides by 39.
x = 4
Now that we know the value of x, we substitute x in each angle measure with its value and find each angle measure.
m<A = 40x - 21 = 40(4) - 21 = 160 -21 = 139
m<B = 31 - 2x = 31 - 2(4) = 31 - 8 = 23
m<C = x + 14 = 4 + 14 = 18
Answer:
m<A = 139; m<B = 23; m<C = 18
