The diagonals of a rectangle ABCD meet at O, If =44^ , find . - Vidyadip

Question

The diagonals of a rectangle ABCD meet at O, If $\angle\text{BOC}=44^\circ,$ find $\angle\text{OAD}.$

✓

Answer

The rectangle ABCD is given as:

We have, $\angle\text{BOC}+\angle\text{BOA}=180^\circ$ (Linear pair) $44^\circ+\angle\text{BOA}=180^\circ$ $\angle\text{BOA}=180^\circ-44^\circ$ $\angle\text{BOA}=136^\circ$ Since, diagonals of a rectangle are equal and they bisect each other. Therefore, in $\triangle\text{OAB},$ we have OA = OB (Angles opposite to equal sides are equal.) Therefore, $\angle1=\angle2$ Now,in $\triangle\text{OAB},$ we have $\angle\text{BOA}+\angle1+\angle2=180^\circ$ $\angle\text{BOA}+2\angle1=180^\circ$ $2\angle1=44^\circ$ $\angle1=22^\circ$ Since, each angle of a rectangle is a right angle. Therefore, $\angle\text{BAD}=90^\circ$ $\angle1+\angle3=90^\circ$ $22^\circ+\angle3=90^\circ$ $\angle3=68^\circ$ Thus, $\angle\text{OAD}=68^\circ$ Hence, the measure of $\angle\text{OAD}$ is 68º. $\angle\text{C}+\angle\text{D}=150^\circ$ Hence, the sum of $\angle\text{C}$ and $\angle\text{D}$ is 150º.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Quadrilaterals→Quadrilaterals — all question types→Maths STD 9 question papers→CBSE Board STD 9 question papers→CBSE Board question paper generator→

Similar questions

Using factor theorem, factorize the following polynomials: $x^3 + 13x^2 + 32x + 20$

In figure, Triangle $\text{ABC}$ is a right angled triangle at $B$. Given that $AB = 9\ cm, AC = 15\ cm$ and $D, E$ are the mid$-$points of the sides $AB$ and $AC$ respectively, calculate
$i.$ The length of $BC$
$ii.$ The area of $\triangle\text{ADE}.$

Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.

Weight (in kg)	No. of students
Below $30$	$0$
Below $30$	$24$
Below $35$	$78$
Below $40$	$183$
Below $45$	$294$
Below $50$	$408$
Below $55$	$543$
Below $60$	$621$
Below $65$	$674$
Below $70$	$685$

The perimeter of an isosceles triangle is $32\ cm$. The ratio of the equal side to its base is $3 : 2$. Find the area of the triangle.

Draw a line segment $AB$ of $4\ cm$ in length. Draw a line perpendicular to $AB$ through $A$ and $B$, respectively. Are these lines parallel?

$ABCD$ is a square, $X$ and $Y$ are points on sides $AD$ and $BC$ respectively such that $\text{AY}=\text{BX}.$ prove that $\text{BY}=\text{AX}$ and $\angle\text{BAY}=\angle\text{ABX}.$

A cylindrical bucket, $28\ cm$ in diameter and $72\ cm$ and high, is full of water. The water is emptied into a rectangular tank, $66\ cm$ long and $28\ cm$ wide. Find the height of the water level in the tank.

In a parallelogram $ABCD$, the bisector of $\angle\text{A}$ also bisects $BC$ at $X$. Find $AB : AD$.

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are $14\ cm, 10\ cm$ and $6cm$. Find the area of the triangle.

If $\text{x}=9-4\sqrt{5},$ find the value of $\text{x}^2-\frac{1}{\text{x}^2}.$