Answer:
∠K = 123°
∠L = 97°
∠O = 83°
∠N = 40°
Step-by-step explanation:
∠K and ∡57° are Supplementary, so their sum is equal to 180°
180 - 57 = 123
∠K = 123°
∠N and ∡140° are also Supplementary
180 - 140 = 40
∠N = 40°
The area of a triangle is equal to 180 when all angles are added together
40 + 57 = 97
180 - 97 = 83
∠O = 83°
∠L is an outside angle, which is equal to the sum of the 2 further angles (in this case ∡57° and ∠N) which we found was 97° when solving for ∠O
∠L = 97°
Now to check ∠K we add ∠O and ∠N
83 + 40 = 123
Now we also check ∠O with ∡140°
140 - 57 = 83
So all of the angles check out correctly
