Construction of Special Angles without Using Protractor

Q. Choose the angles which can be constructed with the help of a ruler and compass.

1. ${30}^{\circ }$
2. ${110}^{\circ }$
3. ${90}^{\circ }$
4. ${120}^{\circ }$

Q.

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

1. ${55}^{\circ }$

2. ${45}^{\circ }$
3. ${75}^{\circ }$
4. ${60}^{\circ }$

Q. Two poles, 18m and 13m high, stand upright in a playground. If their feet are 12m apart find the distance between the poles

Q. Study the steps of construction given.
Step 1: Draw a ray OA.
Step 2: With O as centre and any convenient radius draw an arc MN to cut OA at M.
Step 3: With M as centre and the same radius draw an arc to cut MN at P.
Step 4: With P as centre and the same radius, draw an arc to cut MN at Q.
Step 5: Draw OQ and produce it to D. An angle AOD is constructed.
What is the measure of ∠AOD?

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${120}^{\circ }$
4. ${45}^{\circ }$

Q.

An angle of $85°$can be constructed using ruler and compass. Is it true or false?

1. True
2. False

Q. The line segment BD = ________ in the given diagram.

1. AB + AC
2. AB - AC
3. AD
4. AC - AB

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

1. 35°

2. 45°
3. 90°
4. 180°

Q.

In order to construct a ${90}^{\circ }$ angle, we draw a straight line first. The angle measure of a straight line is ___ (in degrees).

1. ${270}^{\circ }$
2. ${180}^{\circ }$
3. ${45}^{\circ }$

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

Q.

Which one of the following angles can be constructed using a compass and a ruler?

1. 30º

2. 15º

3. 150º

4. 45º

Q.

For the construction of a ${60}^{\circ }$ angle, drawing which of the following is the starting step?

1. line segment

2. None of these

3. arc

4. an angle

Q.

For constructing a right angle without a protractor, which of the following method/s is/are used?

1. Angle Bisector

2. ${60}^{\circ }$ angle construction

3. Median

4. Construction of triangle

Q.

During construction of ${60}^{\circ }$ angle 3 arcs need to be drawn.

1. True

2. False

Q. Construct $\Delta$ABC such that AB = 6.5 cm, $\angle A$ = 45°, and $\angle B$ = 60°. The length of AC is .

1. 5.8 cm
2. 6.5 cm
3. 4.3 cm

Q.

In the process of construction of ${45}^{\circ }$, which angle would be constructed first?

1. ${60}^{\circ }$
2. ${90}^{\circ }$
3. ${30}^{\circ }$
4. ${120}^{\circ }$

Q.

In a straight line, what is the first basic angle that would be obtained? (in degrees)

1. ${180}^{\circ }$
2. ${270}^{\circ }$
3. ${45}^{\circ }$

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

2. ${60}^{\circ }$

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

4. ${120}^{\circ }$

Q. With a ruler and compass which of the following angle cannot be constructed?

1. ${80}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$
4. ${105}^{\circ }$

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. 45º

2. 75º

3. 60º

4. 30º

Q.

If $\angle APB={60}^{\circ }$ and with B as the centre and any radius more than half of AB, another arc is drawn as shown. Taking A as the centre and the same radius as above, cut the previously drawn arc in Y and PY is drawn.

What will be the value of $\angle BPY$?

1. ${30}^{\circ }$

2. ${60}^{\circ }$

3. ${90}^{\circ }$

4. ${180}^{\circ }$

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. Observe the given construction, AF is the angular bisector of $\angle BAE$ and AC is the angular bisector of $\angle BAF$. If $\angle BAE$ = ${60}^{\circ }$, then $\angle BAC$ will be

1. ${60}^{\circ }$
2. ${15}^{\circ }$
3. ${30}^{\circ }$
4. ${10}^{\circ }$

Q. Which of the following angles (in degrees) can be drawn using a ruler and compass.

1. 15°
2. 150°
3. 21°
   
4. 51°
   
5. 7.5°
   
6. 90°
   
7. 120°
   
8. 45°
   

Q.

Construct $△\mathrm{ABC}$ in which $\mathrm{BC}=4.6\mathrm{cm}$, $\angle \mathrm{B}=60°$ and $\angle \mathrm{C}=45°$.

Q. ${120}^{\circ }$ can be produced by extending the arc of

1. ${90}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$

Q. During the construction of a triangle given its base, a base angle and the sum of other two sides, which of the triangles formed are congruent?​

1. $△ABC\&△AMC$
2. $△AMC\&△AMD$
3. $△ABC\&△ADC$
4. $△ABC\&△AMD$