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Which of the following is done to draw an angle of 150∘ using compasses and a ruler?
- a)Bisecting 120∘ and 180∘ angles.
- b)Bisecting 60∘ and 120∘ angles.
- c)Bisecting 0∘ and 60∘ angles.
- d)Bisecting a 360∘ angle.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Which of the following is done to draw an angle of150using compasses a...
To draw an angle of 150° using compasses and a ruler, we need to follow the process of bisecting a 120° and 180° angle.
Here is a step-by-step explanation of how to draw an angle of 150° using compasses and a ruler:
1. Draw a line segment AB using a ruler.
2. Place the compasses on point A and draw an arc that intersects AB.
3. Without changing the compasses' width, place the compasses on point B and draw another arc that intersects the first arc.
4. Label the point where the two arcs intersect as C.
5. Place the compasses on point C and draw an arc that intersects the first arc.
6. Without changing the compasses' width, place the compasses on point B and draw another arc that intersects the second arc.
7. Label the point where the two arcs intersect as D.
8. Draw a line segment CD using a ruler.
9. Label the point of intersection between AB and CD as E.
Now, we have created a 120° angle ACE.
10. Place the compasses on point E and draw an arc that intersects AB.
11. Without changing the compasses' width, place the compasses on point A and draw another arc that intersects the first arc.
12. Label the point where the two arcs intersect as F.
13. Draw a line segment EF using a ruler.
Now, we have bisected the 120° angle ACE into two equal angles, which are each 60°. The angle EAF is 60°.
14. Place the compasses on point E and draw an arc that intersects CD.
15. Without changing the compasses' width, place the compasses on point D and draw another arc that intersects the first arc.
16. Label the point where the two arcs intersect as G.
17. Draw a line segment EG using a ruler.
Now, we have bisected the 60° angle EAF into two equal angles, which are each 30°. The angle EAG is 30°.
18. Place the compasses on point E and draw an arc that intersects AB.
19. Without changing the compasses' width, place the compasses on point A and draw another arc that intersects the first arc.
20. Label the point where the two arcs intersect as H.
21. Draw a line segment EH using a ruler.
Now, we have bisected the 30° angle EAG into two equal angles, which are each 15°. The angle EAH is 15°.
22. Measure the angle EAH using a protractor, and it will measure 15°.
Therefore, by bisecting a 120° angle and then bisecting the resulting 60° angle, we can construct an angle of 150° using compasses and a ruler.
Here is a step-by-step explanation of how to draw an angle of 150° using compasses and a ruler:
1. Draw a line segment AB using a ruler.
2. Place the compasses on point A and draw an arc that intersects AB.
3. Without changing the compasses' width, place the compasses on point B and draw another arc that intersects the first arc.
4. Label the point where the two arcs intersect as C.
5. Place the compasses on point C and draw an arc that intersects the first arc.
6. Without changing the compasses' width, place the compasses on point B and draw another arc that intersects the second arc.
7. Label the point where the two arcs intersect as D.
8. Draw a line segment CD using a ruler.
9. Label the point of intersection between AB and CD as E.
Now, we have created a 120° angle ACE.
10. Place the compasses on point E and draw an arc that intersects AB.
11. Without changing the compasses' width, place the compasses on point A and draw another arc that intersects the first arc.
12. Label the point where the two arcs intersect as F.
13. Draw a line segment EF using a ruler.
Now, we have bisected the 120° angle ACE into two equal angles, which are each 60°. The angle EAF is 60°.
14. Place the compasses on point E and draw an arc that intersects CD.
15. Without changing the compasses' width, place the compasses on point D and draw another arc that intersects the first arc.
16. Label the point where the two arcs intersect as G.
17. Draw a line segment EG using a ruler.
Now, we have bisected the 60° angle EAF into two equal angles, which are each 30°. The angle EAG is 30°.
18. Place the compasses on point E and draw an arc that intersects AB.
19. Without changing the compasses' width, place the compasses on point A and draw another arc that intersects the first arc.
20. Label the point where the two arcs intersect as H.
21. Draw a line segment EH using a ruler.
Now, we have bisected the 30° angle EAG into two equal angles, which are each 15°. The angle EAH is 15°.
22. Measure the angle EAH using a protractor, and it will measure 15°.
Therefore, by bisecting a 120° angle and then bisecting the resulting 60° angle, we can construct an angle of 150° using compasses and a ruler.
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Which of the following is done to draw an angle of150using compasses a...
The correct answer is option 'A'.
Because after bisecting 120⁰ and 180⁰, we get 60⁰ and 90⁰.
Now, 60⁰ + 90⁰ = 150⁰.
Because after bisecting 120⁰ and 180⁰, we get 60⁰ and 90⁰.
Now, 60⁰ + 90⁰ = 150⁰.
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