# Construction of Angles

## Trending Questions

**Q.**

Draw a line AB. At A, draw an arc of length 3 cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure ∠QAB. What is the value of ∠QAB.

120º

30º

90º

60º

**Q.**

Question 84

Draw an angle of 60∘ using ruler and compass and divide it into four equal parts. Measure each part.

**Q.**

Draw an angle of $70\xc2\xb0$. Make a copy of it using only a straight edge and compasses.

**Q.**

A 40∘ angle can be drawn by drawing the angle bisector of a given 80∘ angle.

True

False

**Q.**

For constructing an angle of measure 105∘ using a compass, you need to construct a 60∘ angle too.

**Q.**Which of the following angle cannot be constructed using a compass and a ruler?

35∘

45∘

90∘

180∘

**Q.**Fill in the blanks to complete the steps for construction of angle.

**Steps for construction:**

**A.**Draw a ray QP.

**B.**Draw an arc by taking as________centre with any convenient radius, which intersects QP at point N.

**C.**Taking_______as the centre and the same radius as before, draw another arc which intersects the previous arc at point M.

**D.**Draw QM and produce it to point R.

∠ PQR is an angle of measure.

**Q.**

For the construction of an angle of measure 2212∘ using a compass, which of the following angle should be constructed first?

**Q.**

Draw a line AB. At A, draw an arc of length 3cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure ∠QAB. What is the value of ∠QAB.

30∘

90∘

60∘

120∘

**Q.**

Construct with ruler and compasses 60∘, 45∘ and 30∘ angles. [3 MARKS]

**Q.**Question 1

Construct an angle of 90∘ at the initial point of a given ray and justify the construction.

**Q.**

A ray OC is constructed on the line segment AB such that ∠BOC is x∘. What will be the measure of ∠AOC in terms of x?

x

^{o}90

^{o}- x^{o}180

^{o}- x^{o}360

^{o}- x^{o}

**Q.**

Draw a line AB. At A, draw an arc of length 3cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. Join A and P. Using the protractor, measure ∠PAB. What is the value of ∠PAB.

15∘

30∘

60∘

75∘

**Q.**Draw a line AB. At A, draw an arc of length 3 cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure ∠QAB. What is the value of ∠QAB.

**Q.**

Which of the following angles can be constructed without using a protractor?

30∘

40∘

- 50∘
- 60∘

**Q.**

Draw a line AB. At A, draw an arc of length 3cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure ∠QAB. What is the value of ∠QAB?

30º

60º

90º

120º

**Q.**

Draw a line AB. At A, draw an arc of length 3 cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure ∠QAB. What is the value of ∠QAB.

45∘

60∘

75∘

120∘

**Q.**

Question 2

Construct an angle of 45∘ at the initial point of a given ray and justify the construction.

**Q.**

With a ruler and compass which of the following angles cannot be constructed?

80∘

- 60∘
- 90∘
- 105∘

**Q.**Observe the given construction, AF is the angular bisector of ∠BAE and AC is the angular bisector of ∠BAF. If ∠BAE = 60∘, then ∠BAC will be

- 60∘
- 15∘
- 30∘
- 10∘

**Q.**To construct an angle of 60∘

Steps of construction are:

Step 1: Draw a ray AB

Step 2 will be:

- Taking D as center and any radius, draw an arc intersecting the previous arc at E.
- Taking D as center and same radius, draw an arc intersecting the previous arc at E.
- Taking A as centre and any convenient radius, draw an arc intersecting ray AB at a point D.
- Using protractor, draw an angle 60∘.

**Q.**Which of the following angles can be constructed with the help of simply a ruler and a pair of compass?

- 40∘
- 67.5∘
- 55∘
- 42.5∘

**Q.**

Which one of the following angles can not be constructed using compass and ruler?

- 30∘
- 15∘
- 25∘
- 45∘

**Q.**

For constructing an angle of ∠75∘

Steps of construction are:

Step 1: Draw ray AB

Step 2: Construct ∠BAC=60∘

Step 3 will be

Bisect ∠CAD

Bisect ∠BAC

Construct ∠BAD=90∘

Construct ∠BAD=60∘