Answer:
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