Question

ABCD is a parallelogram in which ∠A = 110°. Find the measure of each of the angles ∠B, ∠C and ∠D.

Answer 1

$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}ABCD\mathrm{is}\mathrm{a}\mathrm{parallelogram}\mathrm{in}\mathrm{which}\angle A\mathrm{is}\mathrm{equal}\mathrm{to}110°. \\ \mathrm{Sum}\mathrm{of}the\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{is}180°. \\ \therefore \angle A+\angle B=180° \\ \Rightarrow 110°+\angle B=180° \\ \Rightarrow \angle B=\left(180°-110°\right) \\ \Rightarrow \angle B=70° \\ \therefore \angle B=70° \end{gathered}$$

$$\begin{gathered} \mathrm{Also},\angle B+\angle C=180° \\ \Rightarrow 70°+\angle C=180° \\ \Rightarrow \angle C=\left(180°-70°\right) \\ \Rightarrow \angle C=110° \\ \therefore \angle C=110° \\ \mathrm{Further},\angle C+\angle D=180° \\ \Rightarrow 110°+\angle D=180° \\ \Rightarrow \angle D=\left(180°-110°\right) \\ \Rightarrow \angle D=70° \\ \therefore \angle D=70° \end{gathered}$$