Question

Provide the missing statement and reasons for the following proof:
Given: ∠A + ∠B = ∠D
prove: ∠C + ∠A + ∠B = 180

Answer 1

Step-by-step explanation:

Statement: ∠C + ∠A + ∠B = 180

Reasons:

1. Given: ∠A + ∠B = ∠D (Given information)

2. Subtracting ∠A and ∠B from both sides of the equation in statement 1, we get: ∠C + (∠A + ∠B) = 180 (Addition property of equality)

3. Substituting the given information from statement 1 into statement 2, we get: ∠C + ∠D = 180

4. Rearranging the terms in statement 3, we get: ∠C + ∠A + ∠B = 180 (Associative property of addition).