Construction of angles

Q.

Draw a circle of any radius, say $4cm$. Draw any two of its diameters. Join the ends of these diameters. What figure do you obtain? What figure is obtained if the diameters are perpendicular to each other?

Q.

Which of the following angles cannot be constructed using ruler and compass?

1. ${15}^{°}$

2. ${45}^{°}$

3. ${75}^{°}$

4. ${85}^{°}$

Q. To construct an angle of ${60}^{\circ }$

Steps of construction are:
Step1: Draw a ray AB.
What is the step 2 for construction?

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

Q.

The semicircular shaped instrument is called ____.

Q.

Question 1

Which of the following are models for perpendicular lines

(a) The adjacent edges of a tabletop.

(b) The lines of a railway track.

(c) The line segments forming the letter ‘L’.

(d) The letter V.

Q.

Fill in the blank with acute, obtuse, right, reflex or straight angle.

When two right angles are added, they form a ________ .

Q.

Using which of the following, it is not possible to construct a ${60}^{\circ }$ angle?

1. Protractor, Ruler

2. Compass, Ruler

3. Set Square (30º-60º-90º)

4. Set Square (45º-45º-90º)

Q.

To construct an angle of ${60}^{\circ }$ using a compass.

Steps of construction are:
Step1: Draw a ray AB
Step 2: ___

Step 3: With A as the centre and same radius draw an arc intersecting the previous arc at E.

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

Q.

What is the sum of the angles formed at intersecting of two lines?

Q. Draw an angle ABC of measure ${45}^o$, Using ruler and compasses. Now draw an angle DBA of measure ${30}^o$ using ruler and compasses as shown in fig 9.23.
What is the measure of $\angle DBC$

Q.

Follow the following steps of constructions:
(a) Draw a line l and mention a point O on it.
(b) With O as center and a short radius, draw an arc that cuts line l at A.
(c) With A as center and the same radius (as in step 2), draw an arc that cuts the first arc at B.
(d) Join O and B. Extend OB to get a ray.
What is the measure of ∠AOB (in degrees)?

1. 45

2. 60

3. 75

4. 90

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 $\angle QAB$. What is the measure of $\angle QAB$ ?

1. ${120}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. ${75}^{\circ }$

Q. Which of the following is an angle that can be constructed using a compass and a ruler?

1. 60⁰
2. 80⁰
3. 20⁰
4. 110⁰

Q.

Follow the following steps of constructions:

1) Draw a line segment OA.

2) With O as center and a short radius, draw an arc that cuts OA at B.

3) With B as center and the same radius (as in step 2), draw an arc that cuts the first arc at C.

4) With C as center and the same radius (as in step 2), draw an arc that cuts the first arc at D.

5) With C and D as centers, draw two arcs with equal radii such that they intersect at E.

6) Join O and E. What’s the measure of $\angle AOE$ ?

1. ${60}^{\circ }$

2. ${45}^{\circ }$

3. ${75}^{\circ }$

4. ${90}^{\circ }$

Q.

Follow the following steps of constructions:
(a) Draw a line l and mention a point O on it.
(b) With O as center and a short radius, draw an arc that cuts line l at A.
(c) With A as center and the same radius (as in step 2), draw an arc that cuts the first arc at B.
(d) Join O and B. Extend OB to get a ray.
What is the measure of ∠AOB (in degrees)?

1. 45

2. 60

3. 75

4. 90

Q. Minimum number of arcs drawn in the construction of 120 degree angle are _______.

1. 2
2. 3
3. 4
4. 6

Q. Using ruler and compasses, construct the following angles:
${180}^o$

Q.

Follow the following steps of constructions:
(a) Draw a line l and mention a point O on it.
(b) With O as center and a short radius, draw an arc that cuts line l at A.
(c) With A as center and the same radius (as in step 2), draw an arc that cuts the first arc at B.
(d) Join O and B. Extend OB to get a ray.
What is the measure of ∠AOB (in degrees)?

1. 45

2. 60

3. 75

4. 90

Q.

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

1. ${30}^{\circ }$
2. ${15}^{\circ }$
3. ${25}^{\circ }$
4. ${45}^{\circ }$

Q. The minimum number of arcs required to draw an angle of 120° is ________.

1. 2
2. 6
3. 3
4. 4

Q.

Follow the following steps of constructions:

1) Draw a line segment OA.

2) With O as center and a short radius, draw an arc that cuts OA at B.

3) With B as center and the same radius (as in step 2), draw an arc that cuts the first arc at C.

4) With C as center and the same radius (as in step 2), draw an arc that cuts the first arc at D.

5) With C and D as centers, draw two arcs with equal radii such that they intersect at E.

6) Join O and E. What’s the measure of $\angle AOE$ ?

1. ${60}^{\circ }$

2. ${45}^{\circ }$

3. ${75}^{\circ }$

4. ${90}^{\circ }$

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 $\angle PAB$. What is the value of $\angle PAB$.

1. 30º

2. 75º

3. 45º

4. 60º

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 $\angle PAB$. What is the value of $\angle PAB$.

1. 30º

2. 45º

3. 60º

4. 75º

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 $\angle QAB$. What is the value of $\angle QAB$.

1. ${60}^{\circ }$

2. ${90}^{\circ }$

3. ${120}^{\circ }$

4. ${30}^{\circ }$

Q.

Which of the following angles (in degree) cannot be constructed using compass and ruler?

1. 90

2. 15

3. 20

4. 45