Question

5)
in the parallelogram (labeled with vertices a, b, c, d), angle at a is (4y + 4)°, angle at b is (3y - 20)°, angle at d is (2x + 6)°, angle at c is (4x)°.
find:
x =
y =
∠a =
∠b =
∠c =
∠d =

Explanation:

Step1: Solve for x (consecutive angles sum to 180°)

$2x + 6 + 4x = 180$
$6x + 6 = 180$
$6x = 174$
$x = \frac{174}{6} = 29$

Step2: Solve for y (consecutive angles sum to 180°)

$4y + 4 + 3y - 20 = 180$
$7y - 16 = 180$
$7y = 196$
$y = \frac{196}{7} = 28$

Step3: Calculate $\angle A$

$\angle A = (4y + 4)^\circ = (4\times28 + 4)^\circ = (112 + 4)^\circ = 116^\circ$

Step4: Calculate $\angle B$

$\angle B = (3y - 20)^\circ = (3\times28 - 20)^\circ = (84 - 20)^\circ = 64^\circ$

Step5: Calculate $\angle C$ (opposite to $\angle A$)

$\angle C = \angle A = 116^\circ$

Step6: Calculate $\angle D$ (opposite to $\angle B$)

$\angle D = \angle B = 64^\circ$

Answer:

$x = 29$
$y = 28$
$\angle A = 116^\circ$
$\angle B = 64^\circ$
$\angle C = 116^\circ$
$\angle D = 64^\circ$