Constructing an Angle

Q.

It is possible to construct an angle equal to ${7.5}^{\circ }$ using compass and ruler.

1. True

2. False

Q. A triangle in which all sides are equal and each interior angle = ${60}^{\circ }$ is called a/an triangle

1. Equilateral
2. Scalene
3. Isosceles

Q.

In the adjoining figure $p\left|\right|q$, $\angle 1=100°$ and $\angle 2=150°$find $\angle x,\angle y,and\angle z.$

Q.

Continuing with the previous question, what angle do we have at the end of four arcs?

With B as the centre and any radius more than half of AB, draw another arc as shown. This is the third arc. With A as the centre and the same radius as above, cut the previously drawn arc in Y. This would be the fourth arc. Join PY.

What is the angle ∠ YPA?

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

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

3. ${180}^{\circ }$

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

Q. Question 1
Write True or False and give reasons for your answer:

An angle of ${52.5}^{\circ }$ can be constructed.

Q.

If m $\angle A={53}^o$ and m $\angle B={35}^o$, then m $\angle A>$m $\angle B$.

1. True
2. False

Q. Draw an angle of measure ${147}^{\circ }$ and construct its bisector.

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.

The steps to construct ${75}^{\circ }$ angle is given below. Arrange these steps in the correct sequence.

1. At the point O, draw an angle AOE = ${60}^{\circ }$.

2. Bisect the ∠DOE.

3. Draw an angle AOD = ${90}^{\circ }$ at a point O on the line segment OA.

1. 3, 2, 1

2. 1, 2, 3

3. 2, 1, 3

4. 3, 1, 2

Q.

If ∠A = 65° and ∠B = 56° then is it true that ∠A > ∠B ?

Q.

Say True or False:

If $m\angle A=530$ and $m\angle B=350$, then $m\angle A>m\angle B.$

1. True
2. False

Q. We cannot draw $\angle {180}^{\circ }$ without using a protactor or a compass.

1. False
2. True

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

Steps of construction are:
Step 1: Draw a ray AB
Step 2 will be:

1. Taking D as center and any radius, draw an arc intersecting the previous arc at E.
2. Using protractor, draw an angle ${60}^{\circ }$.
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.

Which of the following is true?

1. Angles forming a linear pair can both be acute angles.

2. If two lines are intersected by a transversal, then corresponding angles are equal.

3. The supplementary angles have their sum equal to $360°$.

4. Two angles are complementary if their sum is $90°$.

Q. To construct a ${135}^{\circ }$ angle using a compass and ruler only, angles are required to be constructed.

1. 110° & 25°
2. 65°& 70°
3. 90°& 45°
4. 100°& 35°

Q. We can construct $\angle {120}^{\circ }$ with the help of a ruler and compass.

1. False
2. True

Q.

To construct 30° which of the following step is necessary?

1. Construction of 90°

2. Construction of 120°

3. Construction of 45°

4. Construction of 60°

Q. In the given figure if $\angle$ BAC = ${60}^{\circ }$, Burst the options that are correct.

1. AB = AC
2. AB < AC
3. AB > AC
4. BC = BA
5. CA =CB
6. $\mathrm{Angle}A=60°$
7. AB>BC
8. AB=BC=CA

Q.

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are :

1. Not equal but supplementary

2. Equal but not supplementary

3. Either equal or supplementary.

4. Neither equal nor supplementary

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°