Consider angles A, B, and C

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

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

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

To find the value of angle C minus angle B, we need to first determine the values of angles A, B, and C.

We are given that angle A is complementary to angle B, which means the sum of angles A and B is 90 degrees (because complementary angles add up to 90 degrees).

We are also given that angle A is supplementary to angle C, which means the sum of angles A and C is 180 degrees (because supplementary angles add up to 180 degrees).

Since we know the sum of angles A and B is 90 degrees, we can say that angle A = 90 - angle B.

Similarly, since we know the sum of angles A and C is 180 degrees, we can say that angle A = 180 - angle C.

Now we can equate these two expressions for angle A:

90 - angle B = 180 - angle C

To find angle C minus angle B, we need to subtract angle B from both sides of the equation:

90 - angle B - angle B = 180 - angle C - angle B

Simplifying this equation gives us:

90 - 2 * angle B = 180 - angle C

Now we can solve for angle C minus angle B by subtracting angle C from both sides of the equation:

90 - 2 * angle B - angle C = 180 - angle C - angle C

Simplifying further:

90 - 2 * angle B - angle C = 180 - 2 * angle C

Finally, subtracting angle C from both sides of the equation gives us:

90 - 2 * angle B - angle C - angle C = 180 - 2 * angle C - angle C

Simplifying:

90 - 2 * angle B - 2 * angle C = 180 - 3 * angle C

Therefore, angle C minus angle B is:

180 - 3 * angle C - (90 - 2 * angle B)

Keep in mind that we cannot determine the specific values of angle C or angle B without additional information.