What is the measure of angle B in the triangle? This triangle is not drawn to scale.

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m∠B=
°

A triangle labeled ABC with the angles A forty degrees, angle B parenthesis two x minus thirty parenthesis degree, angle C parenthesis x plus twenty parenthesis degrees

m∠B is 70°

Step-by-step explanation:

Knowing angle A is 40°, angles B and C combine for the remaining 140°. To figure out what angle B and C are (although this question asks for B, they could very well be the same, and this could be an isosceles triangle!), use the equation (2x - 30) + (x + 20) = 140.

(2x - 30) + (x + 20) = 140 (Combine 2x and x to get 3x.)

3x - 30 + 20 = 140 (Add -30 and 20 to get -10.)

3x - 10 = 140 (Add 10 to both sides. This undoes the -10.)

3x = 140 + 10 (Add 140 and 10 to get 150.)

3x = 150 (Divide both sides by 3. This undoes the multiplication by 3.)

x = 150/3 (Divide 150 by 3 to get 50.)

x = 50

Now that we know what x is, substitute x for 50 in the equation.

(2(50) - 30) + (50 + 20) = 140

(100 - 30) + (50 + 20) = 140

70 + 70 = 140

140 = 140

Both sides are the same, so x is 50, and angle B's (and C's!) measurement is 70°. (So, yes, as I had said, this is an isosceles triangle.)