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Which of the following can be used to construct a 30o angle?
- a)Construct a 60o angle using compasses and bisect it.
- b)Construct a perpendicular bisector of a line segment.
- c)Construct the bisector of any angle.
- d)Construct an angle congruent to any given angle.
Correct answer is option 'A'. Can you explain this answer?
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Which of the following can be used to construct a30oangle?a)Construct ...
Bisecting a 60o angle results in a 30o angle.
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Which of the following can be used to construct a30oangle?a)Construct ...
Constructing a 30° Angle
To construct a 30° angle, we can use the method of constructing a 60° angle and then bisecting it. This can be done using compasses.
Step 1: Constructing a 60° Angle
To construct a 60° angle, follow these steps:
1. Draw a line segment and label the endpoints as A and B.
2. Place the compasses' needle at point A and draw an arc that intersects the line segment at point C.
3. Keeping the same width, place the compasses' needle at point C and draw another arc that intersects the previous arc at point D.
4. Draw a straight line connecting point A and D.
5. This line segment AD forms a 60° angle with the line segment AB.
Step 2: Bisecting the 60° Angle
To bisect the 60° angle and obtain a 30° angle, follow these steps:
1. Place the compasses' needle at point D and draw an arc that intersects the previously drawn line at point E.
2. Without changing the width, place the compasses' needle at point E and draw another arc that intersects the previous arc at point F.
3. Draw a straight line connecting point D and F.
4. The line segment DF bisects the 60° angle, creating two 30° angles.
Therefore, constructing a 30° angle can be achieved by constructing a 60° angle using compasses and then bisecting it.
Explanation:
Option A is the correct answer because it demonstrates the construction method for a 30° angle using compasses and bisecting a 60° angle. The construction involves drawing two arcs of the same width and then connecting the endpoints to form a 60° angle. By bisecting this angle, a 30° angle is obtained. This method is a fundamental geometric technique for constructing angles and is applicable in various mathematical and practical contexts.
To construct a 30° angle, we can use the method of constructing a 60° angle and then bisecting it. This can be done using compasses.
Step 1: Constructing a 60° Angle
To construct a 60° angle, follow these steps:
1. Draw a line segment and label the endpoints as A and B.
2. Place the compasses' needle at point A and draw an arc that intersects the line segment at point C.
3. Keeping the same width, place the compasses' needle at point C and draw another arc that intersects the previous arc at point D.
4. Draw a straight line connecting point A and D.
5. This line segment AD forms a 60° angle with the line segment AB.
Step 2: Bisecting the 60° Angle
To bisect the 60° angle and obtain a 30° angle, follow these steps:
1. Place the compasses' needle at point D and draw an arc that intersects the previously drawn line at point E.
2. Without changing the width, place the compasses' needle at point E and draw another arc that intersects the previous arc at point F.
3. Draw a straight line connecting point D and F.
4. The line segment DF bisects the 60° angle, creating two 30° angles.
Therefore, constructing a 30° angle can be achieved by constructing a 60° angle using compasses and then bisecting it.
Explanation:
Option A is the correct answer because it demonstrates the construction method for a 30° angle using compasses and bisecting a 60° angle. The construction involves drawing two arcs of the same width and then connecting the endpoints to form a 60° angle. By bisecting this angle, a 30° angle is obtained. This method is a fundamental geometric technique for constructing angles and is applicable in various mathematical and practical contexts.
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Which of the following can be used to construct a30oangle?a)Construct a60oangle using compasses and bisect it.b)Construct a perpendicular bisector of a line segment.c)Construct the bisector of any angle.d)Construct an angle congruent to any given angle.Correct answer is option 'A'. Can you explain this answer?
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Which of the following can be used to construct a30oangle?a)Construct a60oangle using compasses and bisect it.b)Construct a perpendicular bisector of a line segment.c)Construct the bisector of any angle.d)Construct an angle congruent to any given angle.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Which of the following can be used to construct a30oangle?a)Construct a60oangle using compasses and bisect it.b)Construct a perpendicular bisector of a line segment.c)Construct the bisector of any angle.d)Construct an angle congruent to any given angle.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Which of the following can be used to construct a30oangle?a)Construct a60oangle using compasses and bisect it.b)Construct a perpendicular bisector of a line segment.c)Construct the bisector of any angle.d)Construct an angle congruent to any given angle.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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