Make an angle of 100°. Bisect it to get an angle of 50°. Show the working for bisection.
Understand the Problem
The question is asking us to construct an angle of 100 degrees, then bisect that angle to create a new angle of 50 degrees, and to detail the steps taken in the process.
Answer
The bisection of a 100-degree angle results in two angles of $50$ degrees each.
Answer for screen readers
The two bisected angles created from the original angle of 100 degrees are each $50$ degrees.
Steps to Solve
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Constructing the 100-Degree Angle
Use a protractor to measure and draw an angle of 100 degrees. Place the protractor's center point at the vertex of the angle and mark the 100-degree point. Draw a line from the vertex through this point.
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Label the Angle
Label the angle as $\angle ABC$, where point $A$ is the vertex, and points $B$ and $C$ are on the lines forming the angle.
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Finding the Bisecting Line
To bisect the angle, use a compass. Place the compass point at point $A$ and draw an arc that intersects both sides of the angle, marking points $D$ and $E$ where the arc crosses lines $AB$ and $AC$.
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Constructing Arcs from Points D and E
Without changing the compass width, place the compass at point $D$ and draw an arc inside the angle. Then move the compass to point $E$ and draw another arc that intersects the first arc inside the angle. Label the intersection point as $F$.
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Drawing the Bisector
Finally, draw a straight line from point $A$ to point $F$. This line bisects the angle, creating two angles of 50 degrees each.
The two bisected angles created from the original angle of 100 degrees are each $50$ degrees.
More Information
The process of angle construction and bisection is fundamental in geometry. Bisecting angles has practical applications in various fields such as architecture, engineering, and design, where precise angles are crucial.
Tips
- Incorrect Arc Crossings: Ensure that arcs drawn from points $D$ and $E$ intersect properly; misplacement can lead to an inaccurate bisector.
- Mislabeling Points: Always label points clearly to avoid confusion when constructing and referencing angles.
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