Q:

# How do you construct a 135-degree angle?

A:

Construct a 135-degree angle by first constructing a 90-degree angle. Construct an angle bisector for one side of the right angle. The angle addition theorem allows addition of the resulting 90-degree and 45-degree angles to create the required angle. The construction takes a few minutes using ruler and compass.

## Keep Learning

1. Draw a line segment

Use the ruler to draw a line-segment. Label the line-segment with X and Y at its endpoints

2. Construct the 90-degree angle

Set the compass to a convenient length. Place the point of the compass on point x and draw an arc that cuts through line-segment XY at a new point, P. Keep the point of the compass on point X and draw an arc above the line. Move the point of the compass to point P and draw an arc intersecting the first arc. Label the intersecting point as Z. Connect X to Z and extend the line to create a right angle.

3. Extend line-segment XY to T

Use the ruler to extend the line segment the opposite direction from Y. Label the new endpoint.

4. Construct the angle-bisector

Place the point of the compass on point X and draw arcs to intersect line-segments XY and XT. Label these intersections as A and B. Place the point of the compass at point A. Draw a new arc near the center of angle TXZ. Repeat with point B. Label this intersection point F. Draw a line segment from X to F and extend the line. Angle FXY is the required 135-degree angle.

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## Related Questions

• A:

A horizontal line runs parallel to the horizon, at a 90 degree angle to a vertical line. A person lying down in a flat position would create a horizontal line; a standing person would create a vertical line.

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• A:

The exterior angle theorem states that an angle exterior to a triangle equals the sum of the two angles not adjacent to it. The theorem’s basis derives from the fact that the sum of all the interior angles in a triangle equals 180 degrees.

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• A:

The angle addition postulates states that if an angle UVW has a point S lying in its interior, then the sum of angle UVS and angle SVW must equal angle UVW, or ?UVS + ?SVW= ?UVW.