Question

Help with #15, please show all work, will mark brainliest!

Answer 1

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°

Answer 2

Answer:

110°

Step-by-step explanation:

Angle A = Angle C

3x + y = 5y + 20

3x = 4y + 20

Angle C + Angle D = 180

5y + 20 + 5x + 10 = 180

5x + 5y = 150

x + y = 30

x = 30 - y

3(30 - y) = 4y + 20

90 - 3y = 4y + 20

7y = 70

y = 10

x = 30 - 10

x = 20

Angle B = Angle D

= 5(20) + 10

= 110°