Construction of an Angle of 60 Degrees

Q.

Construct a triangle $\mathrm{ABC}$ in which $\mathrm{BC}=7\mathrm{cm}$, $\angle \mathrm{B}=75°$and $\mathrm{AB}+\mathrm{AC}=13\mathrm{cm}$.

Q.

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

Q.

For constructing an angle of ${60}^{\circ }$, we need to draw __ arc/arcs.

Q. "All right angles are equal to each other" is a/an __________.

1. axiom
2. theorem
3. postulate
4. proof

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

Q.

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

1. 80°

2. 90°

3. 60°

4. 105°

Q. A ${60}^{\circ }$ angle is constructed with arc radius as 3 cm. Find the perimeter of the $△BOC$.

1. 3 cm
2. 6 cm
3. 9 cm
4. 12 cm

Q.

Question 9
Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.

Q. Sort the steps to construct an angle of ${60}^0$.

1. $\mathrm{Draw}a\mathrm{line}l\mathrm{and}\mathrm{mention}a\mathrm{point}O\mathrm{on}\mathrm{it}.$
2. $\mathrm{Join}O\mathrm{and}B.\mathrm{Extend}\mathrm{OB}\mathrm{to}\mathrm{get}a\mathrm{ray}.$
3. $\mathrm{With}O\mathrm{as}\mathrm{center}\mathrm{and}a\mathrm{short}\mathrm{radius},\mathrm{draw}\mathrm{an}\mathrm{arc}\mathrm{that}\mathrm{cuts}\mathrm{line}l\mathrm{at}A.$
4. $\mathrm{With}A\mathrm{as}\mathrm{center}\mathrm{and}\mathrm{the}\mathrm{same}\mathrm{radius}\left(\mathrm{as}\mathrm{in}\mathrm{step}2\right),\mathrm{draw}\mathrm{an}\mathrm{arc}\mathrm{that}\mathrm{cuts}\mathrm{the}\mathrm{first}\mathrm{arc}\mathrm{at}B.$

Q.

Question 1
Construct an angle of ${90}^{\circ }$ at the initial point of a given ray and justify the construction.

Q. For constructing angle ${75}^{\circ }$
Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct .

1. $\angle BAD=90°$
2. $\angle BAD=30°$
3. $\angle BAD=150°$

Q. For constructing angle ${75}^{\circ }$
Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct .

1. $\angle BAD=90°$
2. $\angle BAD=30°$
3. $\angle BAD=150°$

Q.

Your aim is to construct an angle $\angle$ YPX = ${30}^{\circ }$ using a compass and a straight edge only. What is the total number of arcs (not necessarily equal in length) to be drawn to construct an angle of ${30}^{\circ }$ after drawing the base ray PX?

1. 3 arcs

2. 4 arcs
3. 5 arcs
4. 6 arcs

Q. In the process of construction of ${45}^{\circ }$, which angle (in degrees) would be constructed first?

1. 90

Q.

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

1. False

2. True

Q.

In an art class, suneha sketched a design using geometrical shapes with the help of colours in the following way:

Here, circles in black and blue are the circumcircle and incircle (of the equilateral $\Delta PQR)$ respectively. Then $\angle BAC$ is equal to

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

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

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

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

Q. Construct an angle of the measure ${45}^{\circ }$ with ruler and compasses.

Q.

Your aim is to construct an angle $\angle$ YPX = ${30}^{\circ }$ using a compass and a straight edge only. What is the total number of arcs (not necessarily equal in length) to be drawn to construct an angle of ${30}^{\circ }$ after drawing the base ray PX?

1. 4 arcs
2. 5 arcs
3. 6 arcs

4. 3 arcs

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 constructing angle ${75}^{\circ }$
Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct .

1. $\angle BAD=90°$
2. $\angle BAD=30°$
3. $\angle BAD=150°$

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 the fourth arc. Join PY.

What is the angle $\angle$YPA?

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

2. ${60}^{\circ }$
3. ${180}^{\circ }$
4. ${90}^{\circ }$

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. 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. Question 3
Draw an angle of ${80}^{\circ }$ with the help of protractor. Then, construct angles of
(i) ${40}^{\circ }$
(ii) ${160}^{\circ }$
(iii) ${120}^{\circ }$

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: Construct $\angle BAD={90}^{\circ }$
Step 4 will be

1. Bisect $\angle BAC$
2. Bisect $\angle BAD$
3. Bisect $\angle CAD$
4. Construct $\angle DAE={25}^{\circ }$

Q. For constructing angle ${75}^{\circ }$
Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct _______.

(A) $\angle BAD=90°$
(B) $\angle BAD=30°$
(C) $\angle BAD=150°$
(D) $\angle BAD=45°$
[1 Mark]

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. For constructing an angle of ${75}^{\circ }$.
Steps of construction:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct

1. $\angle BAD=90°$
2. $\angle BAD=90°$
3. $\angle BAD=60°$

Q. Construct an angle of ${45}^{\circ }$ from a horizontal line.

Q. For constructing angle ${75}^{\circ }$
Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct .

1. $\angle BAD=90°$
2. $\angle BAD=30°$
3. $\angle BAD=150°$