Question

Let mA = 40°. If B is a complement of A, and C is a supplement of B, find these measures.

mB = ___ °
mC = ___ °

Answer 1

< A = 40

< B is a complement of < A....so < B = (90 - 40) = 50

< C is a supplement of < B....so < C = (180 - 50) = 130

Answer 2

m∠B = 50°

m∠C = 130°

Explanation:

Given: m∠A = 40°

B is a complement of A, and C is a supplement of B.

∠B is the complement of ∠A. If the two angles are complement, then the angles add up to 90 degrees.

Therefore, m∠A + ∠m∠B = 90°

Now plug in m∠A = 40° and find m∠B

40 + m∠B = 90

Subtract 40 from both sides, we get

m∠B = 90 - 40

m∠B = 50°

Now let's find m∠C.

∠C is a supplement of ∠B.

If the two angles are supplement, then the sum of the angles is 180 degrees.

m∠B + m∠C = 180°

Now plug in m∠B = 50 and find the m∠C

50 + m∠C = 180

Subtracting 50 from both sides, we get

m∠C = 180 - 50

m∠C = 130°