Question

If ∠a is a complement to ∠b and ∠c is complementary to ∠b, then:

a) ∠a = ∠c
b) ∠a ≠ ∠c
c) ∠a + ∠c = 180 degrees
d) Not enough information to determine

Answer 1

If ∠a is a complement to ∠b and ∠c is complementary to ∠b, then ∠a is equal to ∠c.

The correct answer is:

a) ∠a = ∠c

Step-by-step explanation:

To determine the relationship between ∠a and ∠c, we need to understand what it means for two angles to be complementary. Complementary angles are two angles that add up to 90 degrees. So, if ∠a is a complement to ∠b and ∠c is complementary to ∠b, we can conclude that:

∠a + ∠b = 90 degrees

∠c + ∠b = 90 degrees

If we subtract ∠b from both sides of the equations, we get:

∠a = 90 - ∠b

∠c = 90 - ∠b

Therefore, ∠a is equal to ∠c.