Question

In quadrilateral ABCD, measure angle A+measure angle C=120. Find measure angle B+ measure angle D

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that},\mathrm{sum}\mathrm{of}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{quadrilateral}\mathrm{are}{360}^0. \\ \mathrm{So},\mathrm{in}\mathrm{quadrilateral}\mathrm{ABCD}, \\ \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}={360}^0 \\ \Rightarrow \left(\angle \mathrm{A}+\angle \mathrm{C}\right)+\left(\angle \mathrm{B}+\angle \mathrm{D}\right)={360}^0 \\ \Rightarrow {120}^0+\left(\angle \mathrm{B}+\angle \mathrm{D}\right)={360}^0 \\ \Rightarrow \mathbf{\angle }\mathbf{B}\mathbf{+}\mathbf{\angle }\mathbf{D}\mathbf{=}{\mathbf{240}}^{\mathbf{0}} \end{gathered}$$