Question

(90 Points)
Find the value of each variable in the parallelogram

Answer 1

a = 17

k = 60

r = 20

Explanation:

Adjacent angles of a parallelogram sum to 180°.

As angles 3r° and 6r° are adjacent angles:

⇒ 3r° + 6r° = 180°

⇒ 3r + 6r = 180

⇒ 9r = 180

⇒ 9r ÷ 9 = 180 ÷ 9

⇒ r = 20

Substitute the found value of r into the expression for angle 3r°:

⇒ 3(20)° = 60°

Opposite angles in a parallelogram are equal.

As angles 3r° and k° are opposite angles:

⇒ k° = 3r°

⇒ k° = 60°

⇒ k = 60

Opposite sides of a parallelogram are equal in length.

Therefore:

⇒ a + 13 = 30

⇒ a + 13 - 13 = 30- 13

⇒ a = 17