Consider angles A, B, and C

Question

If angle A is complementary to angle B but supplementary to angle C, what is angle C minus angle B? (In degrees)

Answer 1

Sep 10, 2012
so clearly
A+B = 180
B+C = 180
subtract them
A - C = 0
A = C

given: B = 12x+8 , C = 8x - 8

in B+C=180
12x+8 + 8x-8 = 180
20x = 180
x = 9
so C = 72-8 = 64
but A = C
so A = 64

check:
A = 64°
B = 116°
C = 64°
is A+ B = 64+116 = 180 ? YES
is B+C = 116+64 = 180° yes
is A = C ? yes
here

Answer 2

complementary angles add to 90
supplementary angles add to 180, so
A+B = 90
A+C = 180
C-B = (A+C)-(A+B) = 180-90 = 90