Question
Construct an angle of $120^\circ $ and bisect it.
✓
Answer
Steps of construction:
$1.$Draw a ray $QP.$
$2.$With $Q$ as the centre and any convenient radius, draw an arc cutting $QP$ at $N.$
$3.$With $N$ as the centre and the same radius, cut the arc at $A.$ Again, with $A$ as the centre and the same radius, cut the arc at $M.$
$4.$Draw $QM$ and produce it to $R.$
$\angle\text{PQR is 120}^\circ.$
$5.$With $M$ as the centre and radius more than half of $MN,$ draw an arc.
$6.$With $N$ as the centre and the same radius mentioned in step $(5),$ draw another arc, cutting the previously drawn arc at point $X.$
$7.$Draw $QX$ and produce it to point $S.$
Ray $QS$ is a bisector of $\angle\text{PQR}.$ Ray $QS$ is a bisector of $\angle\text{PQR}.$
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
Construct the angle with the help of ruler and compasses only: $30^\circ $
→Find the $HCF$ of the numbers in the following using the division method: $1794, 2346, 4761$
→To fix fence wires in a garden, 70 m long and 50 m wide, Arvind bought metal pipes for posts. He fixed a post every 5 metres apart. Each post was 2 m long. What is total length of the pipes he bought for the posts?
Find the missing numbers:
(a) 5 glasses of juice shared equally among 4 friends is the same as __________ glasses of juice shared equally among 8 friends. So, $\frac{5}{4}=\frac{?}{8}$
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in __________ bags. So, $\frac{4}{3}=\frac{12}{?}$.
(c) 7 rods divided among 5 children is the same as rods divided among children. So, $\frac{7}{5}=$ __________
→(a) 5 glasses of juice shared equally among 4 friends is the same as __________ glasses of juice shared equally among 8 friends. So, $\frac{5}{4}=\frac{?}{8}$
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in __________ bags. So, $\frac{4}{3}=\frac{12}{?}$.
(c) 7 rods divided among 5 children is the same as rods divided among children. So, $\frac{7}{5}=$ __________
Total number of students of a school in different years is shown in the following table:
Represent the above data by a pictograph.
(a) Prepare a pictograph of students using one symbol an icon of a student to represent 100 students and answer the following questions:
(i) How many symbols represent total number of students in the year 2002?
(ii) How many symbols represent total number of students for the year 1998?
| Years | 1996 | 1998 | 2000 | 2002 | 2004 |
| Number of students | 400 | 550 | 450 | 600 | 650 |
(a) Prepare a pictograph of students using one symbol an icon of a student to represent 100 students and answer the following questions:
(i) How many symbols represent total number of students in the year 2002?
(ii) How many symbols represent total number of students for the year 1998?
Draw two intersecting lines $A B$ and $C D$ as shown in Fig. . Measure $\angle A O D$ and $\angle B O C$. Are they equal? Measure $\angle A O C$ and $\angle B O D$. Are they equal? What conclusion can you draw from it?
→ Simplify:
$7\frac{1}{2}-\Big[2\frac{1}{4}\div\Big\{1\frac{1}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\frac{1}{3}-\frac{1}{6}}\Big)\Big\}\Big]$
→→$7\frac{1}{2}-\Big[2\frac{1}{4}\div\Big\{1\frac{1}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\frac{1}{3}-\frac{1}{6}}\Big)\Big\}\Big]$
The sides of a triangle are in the ratio $2 : 3 : 5.$ If its perimeter is $100\ cm,$ the length of its smallest side is:
→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?