A diagonal of a rectangle is inclined to one | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $^{\circ}$)

Similar Questions

$(1)$ If no three points out of four coplanar points are collinear,then a $\ldots \ldots \ldots$ figure formed by joining these four points in order is called a quadrilateral.
$(2)$ $A$ quadrilateral has $\ldots \ldots \ldots$ pairs of opposite sides.

State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a parallelogram. If $AB = 12 \text{ cm}$ and $BC = 5 \text{ cm}$,then $AC = 13 \text{ cm}$.
$(2)$ $ABCD$ is a trapezium. If $AB \parallel CD$ and $AB = 10 \text{ cm}$,then $CD = 10 \text{ cm}$.

In quadrilateral $ABCD$, one of its diagonals $AC$ measures $20 \, cm$. The altitudes on $AC$ from vertices $B$ and $D$ are $8 \, cm$ and $12 \, cm$ respectively. Find the area of quadrilateral $ABCD$ in $cm^2$.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Perimeter of rectangle $PQRS$ is $40\, cm$. If $PQ : QR = 3 : 5$,then $RS = \ldots \ldots \ldots \, cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module