Question

There are angles whose measures add to 180°. Their measures are angle A=67°, angle B=(2x+20)°, and angle C=x°. What is the measure of angle B?

Answer 1

The sum of angle measures in a triangle is always 180°.

Therefore, we have the equation:

Angle A + Angle B + Angle C = 180°

Substituting the given values:

67° + (2x + 20)° + x° = 180°

Combining like terms:

67° + 20° + x° + 2x° = 180°

Simplifying:

87° + 3x° = 180°

Subtracting 87° from both sides:

3x° = 93°

Dividing both sides by 3:

x° = 31°

Substituting x° back into the equation for angle B:

Angle B = 2x + 20°

Angle B = 2(31°) + 20°

Angle B = 62° + 20°

Angle B = 82°

Therefore, the measure of angle B is 82°.