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

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

m<A = 139; m<B = 23; m<C = 18