Question
In the given figure, the isosceles triangle $ABC ≅ EAD.$ The point $E$ is equidistant from both $A$ and $B.$Image
$4.$ What is the value of $x?$
$A. 40^\circ $
$B. 60^\circ $
$C. 70^\circ $
$D. 80^\circ $
$5.$ What is the value of $y?$
$6.$ What is the value of $\angle BDC?$
$A. 30^\circ $
$B. 40^\circ $
$C. 50^\circ $
$D. 70^\circ $

Answer

$4. B. 60^\circ $
$5. 40$
$40^\circ $
$6. A. 30^\circ $

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

Similar questions

A company manufactures wooden boxes. Given below is the picture of an open wooden box.
Image
The height of the box is $25\ cm$
7. What is the surface area $($in $cm^2)$ of the box$?$
$A. 3500$
$B. 4700$
$C. 5900$
$D. 30000$
$8.$ A shopkeeper store cubes in it.
The side length of one cube is $9\ cm$
What would be the maximum number of cubes the shopkeeper can store in a box$? ($All cubes should be inside the box.$)$
$9.$ Rajan packs a football into a cubical cardboard box. The radius of the football is $11\ cm.$ Rajan keeps a margin of $1 \ cm$ from all the sides of the box while packing.
What is the side length of the cardboard box$?$
$A. 11\ cm$
$B. 20\ cm$
$C. 22\ cm$
$D. 24\ cm$
Deep draws the spiral of irrational numbers below on a paper.
Image
4. What is the length of $OE$ in the spiral$?$
5. Simplify:
A.$ -1$
B. $\sqrt{3}-\sqrt{5}$
C. $-4+\sqrt{15}$
D. $4-2 \sqrt{ } 15$
The map shows three cities Conlen $©,$ Stratford $(S),$ and Texhoma $(T)$ on a straight highway.Image
$4.$ Which of the following is true for the length of the highway between them$?$
$A.$ The length of the highway between $C$ and $S$ is equal to the length of the highway between $S$ and $T.$
$B.$ The length of the highway between $C$ and $S$ is three-fourth of the length of the highway between $S$ and $T.$
$C.$ The length of the highway between $S$ and $T$ is the sum of the lengths of the highway between $CT$ and $CS.$
$D.$ The length of the highway between $C$ and $T$ is the sum of the lengths of the highway between $CS$ and $ST.$
$5.$ A number $Y$ is greater than a number $X$ and another number $Z < 0.$
Which of the following relations can be true for a unique value of $Z?$
$A. X × Z = Y × Z$
$B. X ÷ Z = Y ÷ Z$
$C. X – Z = Y$
$D. X + Z = Y$
$6.$ The area of a triangle is equal to the area of a rectangle.
The area of the rectangle is equal to the area of a parallelogram.
What is the relation between the area of the triangle and the area of the parallelogram?
Read the Source Text given below and answer any four questions:

Chocolate is in the form of a quadrilateral with sides $6\ cm$ and $10\ cm, 5\ cm$ and $5\ cm($as shown in the figure$)$ is cut into two parts on one of its diagonal by a lady. Part$-I$ is given to her maid and part $II$ is equally divided among a driver and gardener.

$i.$ Length of $BD:$
$a. 9\ cm$
$b. 8\ cm$
$c. 7\ cm$
$d. 6\ cm$
Area of $\triangle\text{ABC}:$
$a. 24\ cm^2$
$b. 12\ cm^2$
$c. 42\ cm^2$
$d. 21\ cm^2$
The sum of all the angles of a quadrilateral is equal to:
$a. 180^\circ$
$b. 270^\circ$
$c. 360^\circ$
$d. 90^\circ$
A diagonal of a parallelogram divides it into two congruent:
$a.$ Square.
$b.$ Parallelogram.
$c.$ Triangles.
$d.$ Rectangle.
Each angle of the rectangle is:
$a.$ More than $90^\circ$
$b.$ Less than $90^\circ$
$c.$ Equal to $90^\circ$
$d.$ Equal to $45^\circ$
Read the Source/ Text given below and answer any four questions:

 As shown In the village of Surya there was a big pole $PC.$ This pole was tied with a strong wire of $10\ m$ length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of $10\ m$ so that it can reach at point $P$ on the pole and this should make $60^\circ $ with line $AC.$ Answer the following questions:
$i.$ In the $\triangle\text{PAC}$ and $\triangle\text{PBC}$ which side is common?
$a. PC$
$b. AB$
$c.  AC$
$d. BC$
$ii.$ In the $\triangle\text{PAC}$ and $\triangle\text{PBC}$ which angles are given to be equal?
$a. \angle\text{A}=\angle\text{X}$
$b. \angle\text{B}=\angle\text{X}$
$c.  \angle\text{B}=\angle\text{Y}$
d. None
$iii.$ In the figure, $\triangle\text{PAC}$ and $\triangle\text{PBC}$ are congruent due to which criteria$?$
$a. \text{RHS}$
$b. \text{SAS}$
$c.  \text{SSS}$
$d. \text{ASA}$
$iv.$ What is the value of $\angle\text{PBC}\text{?}$
$a. 30^\circ $
$b. 60^\circ $
$c.  90^\circ $
$d. 45^\circ $
$v.$ What is the value of $\angle\text{X}\text{?}$
$a. 45^\circ $
$b. 60^\circ $
$c.  90^\circ $ 
$d. 30^\circ $
Read the Source/ Text given below and answer these questions:
Arun is participating in an $8$ miles walk. The organizers used a square coordinate grid to plot the course. The starting point is at $A (3, 1).$ At $B (3, 4),$ there's a water station to make sure the walkers stay hydrated. From water station, the walkway turns right and at $C (6,4)$ a garden is situated to keep walkers fresh. From the garden, the walkway turns left and finally, Arun reaches at destination $D$ to complete $8$ miles.
$i.$ How far is the water station $B$ from the starting point $A?$
$a. 4$ miles
$b. 3$ miles
$c. 1$ mile
$d. 5$ miles
$ii.$ How far is the water station $B$ from garden $C?$
$a. 3$ miles
$b. 4$ miles
$c. 1$ mile
$d. 5$ miles
$iii.$ What is the abscissa of destination point $D:$
$a. 3$
$b. 5$
$c. 3$
$d. 6$
$iv$. What is the ordinate of destination point $D?$
$a. 3$
$b. 2$
$c. 6$
$d. 5$
$v.$ What are the coordinates of destination point $D?$
$a. (5, 6)$
$b. (6, 5)$
$c. (3, 9)$
$d. (6, 6)$
Read the following text carefully and answer the questions that follow:
Ladli Scheme was launched by the Delhi Government in the year $2008.$ This scheme helps to make women strong and will empower a girl child. This scheme was started in $2008.$
The expenses for the scheme are plotted in the following bar chart.
Image
Image
$i.$ What are the total expenses from $2009$ to $2011?$
$ii.$ What is the percentage of no of expenses in $2009-10$ over the expenses in $2010-11?$
$iii.$ What is the percentage of minimum expenses over the maximum expenses in the period $2007-2011?$
OR
What is the difference of expenses in $2010-11$ and the expenses in $2006-09?$
Draws a graphical representation of the points scored by team $B.$
His graphical representation is given below.
Image
$10.$ Suman says, “Arun’s graphical representation is not appropriate.”
Do you agree with Suman? Mention $YES$ or $NO.$ Give reason to justify your choice.
Read the following text carefully and answer the questions that follow:
In the middle of the city, there was a park $\text{ABCD}$ in the form of a parallelogram form so that $\ce{AB=CD, AB \| CD}$ and $\ce{AD = BC , AD \| BC}$.
Municipality converted this park into a rectangular form by adding land in the form of $\Delta APD$ and $\Delta BCQ$. Both the triangular shape of land were covered by planting flower plants.
Image
$i.$ Show that $\Delta APD$ and $\Delta BQC$ are congruent.
$ii. PD$ is equal to which side?
$iii.$ Show that $\Delta ABC$ and $\Delta CDA$ are congruent.
OR
What is the value of $\angle m ?$