Answer:
To prove that ∠A ≅ ∠C, we can use the information provided:
∠A and ∠B are supplementary angles.
∠B and ∠C are supplementary angles.
First, let's recall the definition of supplementary angles: Two angles are supplementary if the sum of their measures is equal to 180 degrees.
From statement 1, we know that ∠A and ∠B are supplementary angles, so we can write:
∠A + ∠B = 180°
From statement 2, we know that ∠B and ∠C are supplementary angles, so we can write:
∠B + ∠C = 180°
Now, we have two equations:
∠A + ∠B = 180°
∠B + ∠C = 180°
We can subtract equation 1 from equation 2 to eliminate ∠B:
(∠B + ∠C) - (∠A + ∠B) = 180° - 180°
Simplifying:
∠C - ∠A = 0
Now, add ∠A to both sides of the equation:
∠C - ∠A + ∠A = 0 + ∠A
∠C = ∠A
So, we have shown that ∠C is equal to ∠A. Therefore, ∠A ≅ ∠C.