Question

1. complete the two - column proof. given: ∠a and ∠b are supplementary. prove: ∠c + ∠d = 180°. statement reason ∠a and ∠b are supplementary. m∠a + m∠b = 180°. ∠c = ∠a vertical angles are congruent. definition of congruent. m∠c + m∠d = 180°. ∠c and ∠d are supplementary. definition of supplementary angles.

Explanation:

Step1: Given supplementary angles

Given that $\angle ASM$ and $\angle BSK$ are supplementary, so $m\angle ASM + m\angle BSK=180^{\circ}$ (by the definition of supplementary angles).

Step2: Vertical - angle property

Since $\angle ASM\cong\angle KSC$ (vertical angles are congruent), then $m\angle ASM = m\angle KSC$ (by the definition of congruent angles).

Step3: Substitution

Substitute $m\angle ASM$ with $m\angle KSC$ in $m\angle ASM + m\angle BSK = 180^{\circ}$, we get $m\angle KSC+m\angle BSK = 180^{\circ}$.

Step4: Definition of supplementary angles

Since $m\angle KSC+m\angle BSK = 180^{\circ}$, $\angle KSC$ and $\angle BSK$ are supplementary (by the definition of supplementary angles).

Answer:

The proof is completed as above.