Question

In $\square$ABCD, $\angle$A = 120$°$, If $\angle$B = $\angle$C = $\angle$D, then find the measures of $\angle$B, $\angle$C and $\angle$D.

Answer 1

By the angle addition property of a quadrilateral, we have:

$$\begin{gathered} \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}=360° \\ \mathrm{We}\mathrm{know}: \\ \angle \mathrm{A}=120°\mathrm{and}\angle \mathrm{B}=\angle \mathrm{C}=\angle \mathrm{D} \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ 120°+\angle \mathrm{D}+\angle \mathrm{D}+\angle \mathrm{D}=360° \\ \Rightarrow 120°+3\angle \mathrm{D}=360° \\ \Rightarrow 3\angle \mathrm{D}=360°-120° \\ =240° \\ \Rightarrow \angle \mathrm{D}=\frac{240°}{3} \\ =80° \\ \therefore \angle \mathrm{B}=\angle \mathrm{C}=\angle \mathrm{D}=80° \end{gathered}$$