The statements and reasons to prove that m∠B + m∠C+ m∠D = 180 are given in the solutions below;
We are given that;
Statement 1; m∠C + m∠D = m∠A
Reason; Given
Since we want to prove that; m∠B + m∠C+ m∠D = 180
It means that m∠B + m∠A = 180
This is the definition of a linear pair
Statement 2; m∠B and m∠A form a linear pair
Reason; Definition of Linear pair
Since m∠B + m∠A = 180, it means they are supplementary as they sum up to 180
Statement 3; m∠B and m∠A are supplementary
Reason; Definition of supplementary angles
Since m∠B + m∠A = 180 and m∠C + m∠D = m∠A, then we can use substitution property of Equality to get;
Statement 5; m∠B + m∠C+ m∠D = 180
Reason; Substitution Property of Equality
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