A diagonal of a rectangle is inclined to one | vedclass

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Question

(C) Let the rectangle be $ABCD$ with diagonals $AC$ and $BD$ intersecting at $O$.Given that the diagonal $AC$ is inclined to side $AB$ at an angle of

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(C) Let the rectangle be $ABCD$ with diagonals $AC$ and $BD$ intersecting at $O$.Given that the diagonal $AC$ is inclined to side $AB$ at an angle of $25^{\circ}$,so $\angle CAB = 25^{\circ}$.In a rectangle,diagonals are equal and bisect each other,so $OA = OB$.In $	riangle OAB$,since $OA = OB$,the angles opposite to these sides are equal,so $\angle OBA = \angle OAB = 25^{\circ}$.Using the angle sum property in $	riangle OAB$:$\angle AOB = 180^{\circ} - (25^{\circ} + 25^{\circ}) = 180^{\circ} - 50^{\circ} = 130^{\circ}$.Since $\angle AOB$ and $\angle AOD$ form a linear pair:$\angle AOD = 180^{\circ} - \angle AOB = 180^{\circ} - 130^{\circ} = 50^{\circ}$.Thus,the acute angle between the diagonals is $50^{\circ}$.

$A$ diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$. The acute angle between the diagonals is (in $^{\circ}$)

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