Gujarat BoardEnglish MediumSTD 8MATHSQuadrilaterals3 Marks
Question
Find the remaining angles in the following quadrilaterals.
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Answer
Here, XWUV is a rhombus (all sides equal). In $\triangle VUX , UV = UX$, then the angles opposite them are equal. $\begin{array}{l}\therefore \angle U X V=\angle U V X=30^{\circ} \\\angle U X V=\angle W X V=30^{\circ} \ldots\end{array}$ $\qquad$ (The diagonals of a rhombus bisect its angles) Also, $\angle UVX =\angle WVX =30^{\circ}$ $\qquad$ (The diagonals of a rhombus bisect its angles) $\begin{array}{l}\angle E=2 \times \angle UVX=2 \times 30^{\circ}=60^{\circ} \\\angle V=\angle X=60^{\circ} \ldots \ldots \ldots . . \text { (Opposite angles of a rhombus are equal) } \\\angle V+\angle U=180^{\circ} \ldots \ldots \ldots . . \text { (The sum of adjacent angles of a rhombus is } 180^{\circ} \text { ) } \\ 60^{\circ}+\angle U=180^{\circ} \\\angle U=180^{\circ}-60^{\circ} \\\angle U=120^{\circ} \\\angle U=\angle W=120^{\circ} \ldots \ldots \ldots . . \text { (Opposite angles of a rhombus are equal) }\end{array}$
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