Answer
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!!!