Measure of ∠B is 110°
Step-by-step explanation:
- Step 1: Find ∠B of the parallelogram.
In a parallelogram, opposite angles are equal.
⇒ ∠B = ∠D
⇒ ∠B = (5x + 10)°
- Step 2: Use theorems of quadrilaterals to form equations to find x and y.
Now, angles in a parallelogram are equal to 360°.
⇒ ∠A + ∠B + ∠C + ∠D = 360°
⇒ (3x + y)° + (5x + 10)° + (5y + 20)° + (5x + 10)° = 360°
⇒ 13x + 6y + 40° = 360°
⇒ 13x + 6y = 320° ------ (1)
Also, adjacent angles in a parallelogram are supplementary.
⇒ ∠A + ∠D = 180°
⇒ (3x + y)° + (5x + 10)° = 180°
⇒ 8x + y = 170° ----------- (2)
- Step 3: Solve the 2 equations to find x and y.
13x + 6y = 320
48x + 6y = 1020 (After multiplying eq. 2 with 6 to make coefficients equal)
Subtract (2) from (1)
⇒ -35x = -700
∴ x = 20
⇒ (5x + 10)° = 100 + 10 = 110°
