Question

Find the value of x, then find the measure of all 4 angles of the parallelogram.

Answer 1

1) x = 22°

2) Angle B = 123°

3) Angle C = 57°

Step-by-step explanation

For a parallelogram, the opposite angles are equal to each other and the sum of all the angles give 360°.

So, from these, we know that

Angle A = Angle C = (2x + 13)°

Angle D = Angle B = (7x - 31)°

And

Angle A + Angle B + Angle C + Angle D = 360°

(2x + 13)° + (7x - 31)° + (2x + 13)° + (7x - 31)° = 360°

2x + 13° + 7x - 31° + 2x + 13° + 7x - 31° = 360°

2x + 7x + 2x + 7x + 13° - 31° + 13° - 31° = 360°

18x - 36° = 360°

18x = 360° + 36°

18x = 396°

Divide both sides by 18

(18x/18) = (396°/18)

x = 22°

Angle B = 7x - 31° = 7(22°) - 31° = 154° - 31° = 123°

Angle C = 2x + 13° = 2(22°) + 13° = 44° + 13° = 57°

Hope this Helps!!!