Question
Using rulers and compasses only, draw an angle of measure $135^\circ$.
✓
Answer
Steps of construction:
$1.$ Draw a line segment $AB$ and produce $BA$ to $C$.
$2.$ Keeping $A$ as the center and any radius draw an arc which intersects $AC$ at $D$ and $AB$ at $E$.
$3.$ Keeping $D$ and $E$ as center and radius more than half of $DE$ draw arcs which intersect each other at $F$.
$4.$ Join $FA$ which intersects the arc in $(2)$ at $G$.
$5.$ Keeping $G$ and $D$ as center and radius more than half of $GD$ draw arcs which intersect each other at $H$.
$6.$ Join $HA$.
Therefore $\angle\text{HAB}=135^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A line segment $AB$ is of length $5\ cm$. Draw a circle of radius $4\ cm$ passing through $A$ and $B$. Can you draw a circle of radius $2\ cm$ passing through $A$ and $B$? Give reason in support of your answer.
→In a cyclic quadrilateral $ABCD$, if $\angle\text{A}-\angle\text{C}=60^\circ,$ prove that the smaller of two is $60^\circ$
→→
P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.
Find the volume, the lateral surface area and the total surface area of the cuboid whose dimensions are: Length $= 12cm,$ breadth $= 8\ cm$ and height $= 4.5\ cm$
→A conical tent is $10m$ high and the radius of its base is $24\ m$. Find the slant height of the tent. If the cost of $1m^2$ canvas is $₹ 70$, find the cost of canvas required to make the tent. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$
→In the given figure, sides $AD$ and $AB$ of cyclic quadrilateral $ABCD$ are produced to $E$ and Frespectively.
If $\angle\text{CBF}=130^\circ$ and $\angle\text{CDE}=\text{x}^\circ,$ find the value of $x$.
→If $\angle\text{CBF}=130^\circ$ and $\angle\text{CDE}=\text{x}^\circ,$ find the value of $x$.
Two chords $AB$ and $CD$ of lengths $5\ cm$ and $11\ cm$ respectively of a circle are parallel to each other and are opposite side of its centre. If the distance between $AB$ and $CD$ is $6\ cm$, find the radius of the circle.
→The income and expenditure for $5$ years of a family is given in the following data:
Represent the above data by a bar graph.
→|
Years
|
$1995–96$
|
$1996–97$
|
$1997–98$
|
$1998–99$
|
$1999–2000$
|
|
Income (Rs. In thousands)
|
$100$
|
$140$
|
$150$
|
$170$
|
$210$
|
|
Expenditure (Rs. in thousands)
|
$80$
|
$130$
|
$145$
|
$160$
|
$190$
|
The daily minimum temperatures in degrees Celsius recorded in a certain arctic region are as follows:
$-12.5, -10.8, -18.6, -8.4, -10.8, -4.2, -4.8, -6.7, -13.2, -11.8, -2.3, 1.2, 2.6, 0, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -5.8, -8.9, -14.6, -12.3, -11.5, -7.8, -2.9.$
Represent them as frequency distribution table taking $-19.9$ to $-15$ as the first class interval.
→$-12.5, -10.8, -18.6, -8.4, -10.8, -4.2, -4.8, -6.7, -13.2, -11.8, -2.3, 1.2, 2.6, 0, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -5.8, -8.9, -14.6, -12.3, -11.5, -7.8, -2.9.$
Represent them as frequency distribution table taking $-19.9$ to $-15$ as the first class interval.