Find all the other angles inside the following rectangles. - Vidyadip

Question

Find all the other angles inside the following rectangles.

✓

Answer

$\angle POS=\angle ROQ=110^{\circ}$$\qquad$ (Vertically opposite angles)
$\begin{array}{l}\angle POS+\angle POQ=180^{\circ} \ldots \ldots \ldots . . \text { (Linear Pair) } \\110^{\circ}+\angle POQ=180^{\circ} \\\angle POQ=180^{\circ}-110^{\circ} \\\angle POQ=70^{\circ}\end{array}$
$\angle POQ=\angle SOR=70^{\circ}$$\qquad$ (Vertically opposite angles)
In $\triangle POS , OP = OS$, then the angles opposite them are equal.
$\therefore \angle 1=\angle 2=a$
In $\triangle POS$,
$\angle 1+\angle 2+\angle POS =180^{\circ}$ $\qquad$ (Sum of angles of a triangle)
$a+a+110^{\circ}=180^{\circ}$
$2 a =180^{\circ}-110^{\circ}$
$2 a =70^{\circ}$
a $=35^{\circ}$
$\therefore \angle 1=\angle 2= a =35^{\circ}$
$\angle 1=\angle 5=35^{\circ}$ $\qquad$ (Alternate interior angles)
$\angle 2=\angle 6=35^{\circ}$ $\qquad$ (Alternate interior angles)
Since $A B C D$ is a rectangle, $\angle P=90^{\circ}$
$\begin{array}{l}\angle 9=\angle 1+\angle 8 \\90^{\circ}=35^{\circ}+\angle 8 \\\angle 8=90^{\circ}-35^{\circ} \\\angle 8=55^{\circ}\end{array}$
$\angle 8=\angle 4=55^{\circ}$ $\qquad$ (Alternate interior angles)
In $\triangle POQ , OP = OQ$, then the angles opposite them are equal
i.e. $\angle 7=\angle 8=55^{\circ}$
$\angle 7=\angle 2=55^{\circ}$ $\qquad$ (Alternate interior angles)
Thus, $\angle POS =\angle ROQ =110^{\circ}$.
$\begin{array}{l}\angle POQ=\angle SOR=70^{\circ} . \\\angle 1=\angle 2=\angle 5=\angle 6=35^{\circ} . \\\angle 8=\angle 4=\angle 7=\angle 2=55^{\circ} .\end{array}$

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 "5 Marks Questions" from Quadrilaterals→Quadrilaterals — all question types→MATHS STD 8 question papers→Gujarat Board STD 8 question papers→Gujarat Board question paper generator→

Similar questions

Construct a quadrilateral $ABCD$ in which $AB = 3.5\ cm, BC = 3.8\ cm, CD = DA = 4.5\ cm$ and diagonal $BD = 5.6\ cm.$

During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row of the square.

The following table gives the quantity of petrol and its cost. Plot a graph to show the data

No. of litres of petrol	$10$	$15$	$20$	$25$
Cost of petrol in ₹	$500$	$750$	$1000$	$1250$

Find the amount and the compound interest on $Rs. 8000$ for $1\frac{1}{2}$years at $10\%$ per annum, compounded half-yearly.

Ahmed buys a plot of land for $Rs. 480000.$ He sells of it at a loss of $6\%.$ At what gain percent should he sell the remaining part of the plot to gain $10\%$ on the whole$?$

Construct a quadrilateral $ABCD,$ where$\angle\text{A}=65^\circ,\text{B}=105^\circ,\text{C}=75^\circ,$ $BC = 5.7$ and $CD = 6.8\ cm$.

By selling a pair of earnings at a discount of $25\%$ on the marked price, a jeweller makes a profit of $16\%$. If the profit is $Rs. 48$, what is the cost price? What is the marked price and price at which the pair was eventually bought?

By what number should $\Big(\frac{-2}{3}\Big)^{-3}$ be divided so that the quotient may be $\Big(\frac{4}{27}\Big)^{-2}$?

Resolve each of the following quadratic trinomial into factor:
$12x^2- 17xy + 6y^2$

Monu's father is $26$ years younger than Monu's grandfather and $29$ years older than Monu. The sum of the ages of all the three is $135$ years. What is the age of each one of them?