Question

The measure of two angles of a quadrilateral are 105 degree and 45 degree and the other two angles are equal. Find the measure of each of the equal angles.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{ABCD}\mathrm{be}\mathrm{the}\mathrm{quadrilateral}. \\ \mathrm{Let}\angle \mathrm{A}=105°;\angle \mathrm{B}=45° \\ \mathrm{Now},\angle \mathrm{C}=\angle \mathrm{D}=\mathrm{x}\left(\mathrm{say}\right) \\ \mathrm{now}, \\ \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}=360°\mathbf{}\mathbf{}\mathbf{}\mathbf{}\left(\mathbf{Angle}\mathbf{}\mathbf{sum}\mathbf{}\mathbf{property}\right) \\ \Rightarrow 105°+45°+\mathrm{x}+\mathrm{x}=360° \\ \Rightarrow 150°+2\mathrm{x}=360° \\ \Rightarrow 2\mathrm{x}=360°-150° \\ \Rightarrow 2\mathrm{x}=210° \\ \Rightarrow \mathrm{x}=\frac{210°}{2}=105° \\ \mathrm{So},\angle \mathrm{C}=\angle \mathrm{D}=105° \end{gathered}$$