Question
Using ruler and compasses, construct the following angle:
75°
75°
✓
Answer
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre $B$ and a suitable radius draw an arc and cut off $P Q$, then $Q R$ of the same radius.
(iii) With centre Q and R, draw two arcs intersecting each other at S.
(iv) Join SB.
(v) With centre Q and D draw two arcs intersecting each other at T.
(vi) Join $B T$ and produce it to $A$.
Then $\angle A B C=75^{\circ}$.
(i) Draw a line segment BC.
(ii) With centre $B$ and a suitable radius draw an arc and cut off $P Q$, then $Q R$ of the same radius.
(iii) With centre Q and R, draw two arcs intersecting each other at S.
(iv) Join SB.
(v) With centre Q and D draw two arcs intersecting each other at T.
(vi) Join $B T$ and produce it to $A$.
Then $\angle A B C=75^{\circ}$.
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
The length of a rectangular plot exceeds its breadth by 5 m. If the perimeter of the plot is 142 m, find the length and the breadth of the plot.
The sum of three numbers, whose ratios are $3 \frac{1}{3}: 4 \frac{1}{5}: 6 \frac{1}{8}$ is 4917 . Find the numbers.
→Draw a line segment AB = 5.8 cm. Mark a point P in AB such that PB = 3.6 cm. At P, draw a perpendicular to AB.
In the given figure, angle $A D B=90^{\circ}, A C=A B=26 cm$ and $B D=$ $D C$. If the length of $A D=24 cm$; find the length of $B C$.
→In the case, given below, draw a line through point $P$ and parallel to $A B:$
→Draw a line segment of length 6.4 cm. Draw its perpendicular bisector.
Five Students A, B, C, D, and E are competing in a long-distance race. Each student’s probability of winning the race is given below:
A → 20%, B → 22%, C → 7%, D → 15% and E → 36%
(i) Who is most likely to win the race?
(ii) Who is least likely to win the race?
(iii) Find the sum of probabilities given.
(iv) Find the probability that either A or D will win the race.
(v) Let S be the event that B will win the race.
(a) Find P(S)
(b) State, in words, the complementary event S’.
(c) Find P(S’)
A → 20%, B → 22%, C → 7%, D → 15% and E → 36%
(i) Who is most likely to win the race?
(ii) Who is least likely to win the race?
(iii) Find the sum of probabilities given.
(iv) Find the probability that either A or D will win the race.
(v) Let S be the event that B will win the race.
(a) Find P(S)
(b) State, in words, the complementary event S’.
(c) Find P(S’)
A shopkeeper buys an article for ₹ 300. He increases its price by 20% and then gives 10% discount on the new price. Find:
(i) the new price (marked price) of the article.
(ii) the discount is given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.
(i) the new price (marked price) of the article.
(ii) the discount is given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.
Evaluate: $-\frac{5}{7}-\left(-\frac{3}{8}\right)$
→Put the given fraction in ascending order by making denominator equal:
$\frac{5}{7}, \frac{3}{8}, \frac{9}{14} \text { and } \frac{20}{21}$
→$\frac{5}{7}, \frac{3}{8}, \frac{9}{14} \text { and } \frac{20}{21}$