Question

To construct a parallelogram, BC = 4 cm , CD= 3 cm and ∠BCD = ${60}^{\circ }$
Determine all the other angles of the parallelogram.

• A. ∠DAB= ${120}^{\circ }$ ∠ABC = ${60}^{\circ }$ and ∠ADC = ${120}^{\circ }$
• B. ∠DAB= ${100}^{\circ }$ ∠ABC = ${100}^{\circ }$ and ∠ADC = ${100}^{\circ }$
• C. ∠DAB= ${110}^{\circ }$ ∠ABC = ${50}^{\circ }$ and ∠ADC = ${130}^{\circ }$
• D. ∠DAB= ${60}^{\circ }$ ∠ABC = ${120}^{\circ }$ and ∠ADC = ${120}^{\circ }$

Answer 1

The correct option is D ∠DAB= ${60}^{\circ }$ ∠ABC = ${120}^{\circ }$ and ∠ADC = ${120}^{\circ }$

∠DAB = ∠BCD = ${60}^{\circ }$ [ opp angles of a parallelogram are equal]
∠DAB + ∠ABC = ${180}^{\circ }$ [co interior angles are supplementary]
∠ADC =∠ABC = ${120}^{\circ }$ [opp angles of a parallelogram are equal]