Answer:
A. Complementary and Adjacent
B. ∠KLM = 22° and ∠MLN = 68°
Step-by-step explanation:
Question A
As ∠KLN is a right angle, ∠KLN = 90°
⇒ ∠KLM + ∠MLN = 90°
When the sum of two angles is 90°, they are called complementary angles.
∠KLM and ∠MLN have a common side of ML and a common vertex (corner point) L.
When two angles have a common side and a common vertex but do not overlap in any way, the are called adjacent angles.
Question B
First find n:
∠KLM + ∠MLN = ∠KLN
⇒ 2n + (6n + 2) = 90
⇒ 2n + 6n + 2 = 90
Combine like terms:
⇒ 8n + 2 = 90
Subtract 2 from both sides:
⇒ 8n = 88
Divide both sides by 8:
⇒ n = 11
Now substitute the found value of n into the expressions for the two angles:
⇒ ∠KLM = 2(11) = 22°
⇒ ∠MLN = 6(11) + 2 = 68°
