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How to Construct a 75 Degree Angle

Construct a 75 Degree Angle:
By constructing a 90 degree angle using compass with base horizontal to the angle,75 degree angle can be obtained. A bisector angle is produced in between 90 degree angle,which gives an angle of 75 degree.

Construct 75 Degree Angle using Compass

The following steps are carried out to construct 75 degree-angle.

Step 1: Draw a ray with end point  A and B.

Ray Figure

Step 2: With A as center and any radius, draw an arc cutting the ray at point C using a compass.

Radius Figure

Step 3: With C as center and the same radius, draw an arc cutting the arc drawn at D.

The Arc Radius

Step 4: With D as center and the same radius, draw  an arc again intersecting the previously drawn arc at E.

Intersecting Arc

Step 5: Now, take any radius and draw two arcs with D and E as centers. Let these two arcs intersect at a point F.

Radius Intersect

Step 6: Join AF ∠FAB obtained is the angle of measure of 90 degree.

The Angle of Measure

Step 7:The line AF intersect the arc at the point named as G. 

Intersect the Arc Figure

Step 8: With G and D as center draw an arc with radius more than half of the measurement (GD).The arc intersect at the point P.

Radius Measurement Figure

Step 9: Join the point P and A.∠PAB obtained is the angle of measurement 75 degree.

Angle of Measurement

Step 10: 75 degree angle

Degree Angle Figure