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Answer:
Given: ABCD is a parallelogram.
Prove: Angle A and B are supplementary and C and D are supplementary.
That is, m∠A + m∠B = 180° and m∠C + m∠D = 180°
Statement Reason
1. ABCD is a parallelogram 1. Given
2.m∠A=m∠C and m∠B=m∠D 2. Definition of parallelogram.
3.m∠A+m∠B+m∠C+m∠D=360° 3. Definition of quadrilateral
4. m∠A+m∠B+m∠A+m∠B=360° 4. By substitution
⇒ 2( m∠A + m∠B ) = 360°
⇒ m∠A + m∠B = 180°
Similarly, m∠C + m∠D = 180°
5.∠A and ∠C are supplementary, 5. Def. of Supplementary
∠ B and ∠D are supplementary
