Question
Using ruler and compasses only, draw an angle of measure $135^\circ .$
✓
Answer
We draw a line $AB$ and mark a point $O$ on it. With a convenient radius and centre at $O,$ draw an arc $PQ$ with the help of a compass intersecting the line $AB$ at $P$ and $Q.$ With the same radius and centre at $P,$ draw another arc intersecting the arc $PQ$ at $R.$ With the same radius and centre at $Q,$ draw one more arc intersecting the arc $PQ$ at $S,$ opposite to $P.$ Taking $S$ and $R$ as centres and radius more than half of $SR,$ draw two arcs intersecting each other at $T.$ Join $O$ and $T$ intersecting the arc $PQ$ at $C.$ Taking $C$ and $Q$ as centres and radius more than half of $CQ,$ draw two arcs intersecting each other at $D.$ Join $O$ and $D$ and extend it to $X$ to form the ray $OX.$
$\angle\text{AOX}$ is the required angle of measure $135^\circ .$
$\angle\text{AOX}$ is the required angle of measure $135^\circ .$
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
Draw an angle of $60^\circ ,$ using a pair of compasses. Bisect it to make an angle of $30^\circ .$
→Draw number line and locate the points on them: $\frac25,\;\frac35,\frac85,\;\frac45$
→Construct the following angles with the help of a protractor: $45^\circ , 67^\circ , 38^\circ , 110^\circ , 179^\circ , 98^\circ , 84^\circ $
→In a village six fruit merchants sold the number of fruit baskets in a particular season:
Observe this pictograph and answer the question: Which merchant sold the maximum number of baskets?
→| Number of fruit merchants | Number of fruit baskets  $- 100$ Fruit baskets |
| Rahim |  |
| Lakhanpal |  |
| Anwar |  |
| Martin |  |
| Ranjit Singh |  |
| Joseph |  |
Think and mark the positions as directed:
(a) Mark ‘A’ at the point where Akshi will be after she runs 250 m.
(b) Mark ‘B’ at the point where Akshi will be after she runs 500 m.
(c) Now, Akshi ran 1000 m. How many full rounds has she finished running around her track? Mark her position as ‘C’.
(d) Mark ‘X’ at the point where Toshi will be after she runs 250 m.
(e) Mark ‘Y’ at the point where Toshi will be after she runs 500 m.
The lengths in km (rounded to nearest hundred) of some major rivers of India is given below:
Draw a bar graph to represent the above information.
→| River | Length (in km) |
| Narmada | $1300$ |
| Mahanadi | $900$ |
| Brahmputra | $2900$ |
| Ganga | $2500$ |
| Kaveri | $800$ |
| Krishna | $1300$ |
The population of Delhi State in different census years is as given below:
Represent the above information with the help of a bar graph.
→|
Census year
|
$1961$
|
$1971$
|
$1981$
|
$1991$
|
$2001$
|
|
Cars Sold
|
$30$
|
$55$
|
$70$
|
$110$
|
$150$
|
Is there a 4-sided figure in which all the sides are equal in length but is not a square? if such a figure exists, can you construct it?
Draw a line $l.$ Take a point $A,$ not lying on $l.$ Draw a line m such that $\text{m}\perp\text{l}$ and passing through $A.$ Using ruler and a set-square.
→Katrina rode her bicycle $6\frac12 \ km$ in the morning and $8\frac34 \ km$ in the evening. Find the distance travelled by her altogether on that day.
→