Question

One angle of a quadrilateral is 111° and the remaining three angles are equal. Find three angles.

Answer 1

Dear student,

$$\begin{gathered} LetABCDbeaquadrilateralwhose \\ \angle A=111°and\angle B=\angle C=\angle D....\left(i\right) \\ Now, \\ \angle A+\angle B+\angle C+\angle D=360°---(Sumof\angle sofquadrilateralis360°) \\ \Rightarrow 111°+\angle B+\angle B+\angle B=360°--(from(i)) \\ \Rightarrow 3\angle B=360°-111° \\ \Rightarrow 3\angle B=360°-111 \\ \Rightarrow 3\angle B=249 \\ \Rightarrow \angle B=\frac{249}{3}=83° \\ thus,thethreeanglesare\angle B=\angle C=\angle D=83° \end{gathered}$$

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