Question

In a parallelogram ABCD if A=45° then find other angle

Answer 1

$$\begin{gathered} \mathrm{In}\mathrm{the}\mathrm{parallelogram}\mathrm{ABCD},\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\angle \mathrm{A}={45}^{\circ }. \\ \mathrm{As}\mathrm{the}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{are}\mathrm{supplementary},\mathrm{then} \\ \angle \mathrm{A}+\angle \mathrm{B}={180}^{\circ } \\ \Rightarrow {45}^{\circ }+\angle \mathrm{B}={180}^{\circ } \\ \Rightarrow \angle \mathrm{B}={180}^{\circ }-{45}^{\circ }={135}^{\circ }. \\ \mathrm{Also},\angle \mathrm{A}+\angle \mathrm{D}={180}^{\circ }\left[\mathrm{Adjacent}\mathrm{angles}\mathrm{are}\mathrm{supplementary}\right] \\ \Rightarrow {45}^{\circ }+\angle \mathrm{D}={180}^{\circ } \\ \Rightarrow \angle \mathrm{D}={180}^{\circ }-{45}^{\circ }={135}^{\circ }. \\ \mathrm{Now},\angle \mathrm{C}+\angle \mathrm{D}={180}^{\circ }\left[\mathrm{Adjacent}\mathrm{angles}\mathrm{are}\mathrm{supplementary}\right] \\ \Rightarrow {135}^{\circ }+\angle \mathrm{C}={180}^{\circ } \\ \Rightarrow \angle \mathrm{C}={180}^{\circ }-{135}^{\circ }={45}^{\circ }. \end{gathered}$$