Construction of Given Angles from Standard Angles

Q. Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose? [4 MARKS]

Q.

Given a line l and a point M on it, draw a perpendicular MP to l where MP = 5.2 cm and a line q parallel to l through P. [2 MARKS]

Q. With the help of a ruler and a pair of compasses, it is not possible to construct an angle of

1. ${15}^{\circ }$
2. ${75}^{\circ }$
3. ${42.5}^{\circ }$
4. ${105}^{\circ }$

Q.

Which of the following angles can be constructed with the help of a ruler and a compass?

1. ${42.5}^{\circ }$

2. ${40}^{\circ }$

3. ${67.5}^{\circ }$

4. ${55}^{\circ }$

Q.

For making an angle of 105${}^{\circ }$, you need to construct a 60${}^{\circ }$ angle too.

1. True

2. False

Q.

What is the number of arcs that need to be drawn during the construction of a 120-degree angle? __

Q. Steps for the construction of $\angle AOB={120}^{\circ }$ is given below. Choose the correct order.
1.With Q as the centre and with same radius as in step- 3, draw an arc so as to cut the arc drawn in step - 2. Name the point of intersection as R.
2.With P as the centre, draw an arc with the same radius as in step-2 intersecting the previous arc. Name the point of intersection as R.
3.Draw a ray OB
4.Join points O and R using a scale and a pencil. Extend it to get ray OA
5.With O as the centre, draw an arc with suitable radius that cuts OB. Name the point of intersection as P

1. 3, 5, 2, 4, 1
2. 3, 5, 4, 2, 1
3. 3, 5, 2, 1, 4
4. 3, 2, 5, 4, 1

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

1. ${90}^{\circ }$ and ${45}^{\circ }$
2. ${120}^{\circ }$ and ${15}^{\circ }$
3. ${60}^{\circ }$ and ${75}^{\circ }$
4. ${100}^{\circ }$ and ${35}^{\circ }$

Q.

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

${60}^{\circ }$, ${80}^{\circ }$, ${90}^{\circ }$, ${105}^{\circ }$

1. 80°

2. 90°

3. 60°

4. 105°

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

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

Q. With the help of a ruler and a pair of compasses, it is not possible to construct an angle of:

1. ${15}^{\circ }$
2. ${75}^{\circ }$
3. ${42.5}^{\circ }$
4. ${15}^{\circ }$

Q.

A 75${}^{\circ }$ angle can be made by drawing angle bisector between a 90${}^{\circ }$ angle arm and a ___${}^{\circ }$ angle arm.

Q.

Draw a circle with radius $4cm$ and center P. Draw another circle of same radius and with center at Q such that it intersects the previous circle. Join PQ. Now join the points of intersection and name this line segment as AB. Mark the point of intersection of AB and PQ as O.

$\angle$AOP = __${}^{\circ }$

Q. With the help of a ruler and a compass it is not possible to construct an angle of

1. ${37.5}^{\circ }$
2. ${40}^{\circ }$
3. ${22.5}^{\circ }$
4. ${67.5}^{\circ }$

Q.

Observe the given construction, if $\angle BAE={60}^{\circ }$, then $\angle BAC$ will be

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

2. ${15}^{\circ }$

3. ${30}^{\circ }$

4. ${10}^{\circ }$

Q. For constructing an angle of ${75}^{\circ }$

Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3 will be

1. Bisect $\angle BAC$
2. Construct $\angle BAD={90}^{\circ }$
3. Construct $\angle BAD={60}^{\circ }$
4. Bisect $\angle CAD$

Q.

For making an angle of 105${}^{\circ }$, you need to construct a 60${}^{\circ }$ angle too.

1. True

2. False

Q.

Which of the following angles can be constructed with the help of a ruler and a compass?

1. ${42.5}^{\circ }$

2. ${40}^{\circ }$

3. ${67.5}^{\circ }$

4. ${55}^{\circ }$

Q.

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

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

2. 40${}^{\circ }$

3. 50${}^{\circ }$
4. 60${}^{\circ }$