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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

Best Results From Yahoo Answers Youtube

From Yahoo Answers

Question:k i have to construct a 75 degree angle, i knw i need to make a 60 degree anlge and a 15 degree angle but idk how to make that with a compass and ruler. and i cant use a protract. please explain to me how i can construct this. thank you.

Answers:Well, a right angle is 90 degrees Half of 90 is 45 Three 15 degree angles make 45 degrees another one makes 60 15+15+15+15=45 another 15 equals 60 15+15+15+15+15=60 another equals 75 15+15+15+15+15+15=75 90-75=15 so a 75 degree angle is one 15 degree angle short of a right angle



Question:help please!!! my teacher is psycho and doesnt explain how to construct obtuse angle bisectors. i already know how to construct acute angle bisectors like 30,45, and 15 degree angles, but i dont know how to do it to find larger angles!! please help! you can put website links or just explain how to do it by using a straight edge and compass. thank you!

Answers:There isn't any difference between bisecting acute, right, or obtuse angles. As shown here: http://i45.tinypic.com/2dkn5s3.gif You mark a point on each ray at the same distance from the vertex (blue circle). Then you draw a circle from each of those points with equal radii (green circles). The (red) ray from the vertex of the angle through the point(s) where the (green) circles intersect bisects the angle. To construct the angles you name, you can add smaller angles: Construct 60 by drawing a circle, with a diameter. Then draw a 2nd circle of the same radius where the diameter meets the first circle. The line from the center of the first circle to the point where the 2 circles intersect will be at 60 from the original diameter. 120 = 60 + 60 135 = 90 + 45, so bisect a 90 to get 45, then add it on 75 = 45 + 30 105 = 75 + 30 You add angles by copying them onto the sides of others.

Question:i would like to know how to construct: 45 degree angles 105 degree angles 75 degree angles and 90 degree angles can anyone please give me the rules of how to construct those angles or lead me to a website which will help me??i really need help thanks i have to construct it not just take a protractor and draw it in but show how i got it

Answers:Draw a line segment AB. Put your compass point at B and stretch the compass out until it is at point A. Now draw a circle. Now move the compass point to B, leaving the compass opening the same as before and draw another circle. The circles will intersect in two points. Call them C and D. Draw CD and name its intersection with AB as the point E. angle CEB is a right angle. Now you need to bisect the 90 degree angle you just constructed to get two 45 degree angles. Look in your book as to how to bisect an angle. The angle CAB = 60 degrees. So bisect it to get a 30 degree angle and then bisect it to get a 15 degree angle. You can get a 105 degree angle by adding the 90 degree angle and the 15 degree angle. Similarly, you can get a 75 degree angle by subtracting the 15 degree angle from 90 degrees. Look in your book on how to copy an angle.

From Youtube

Constructing a 15 Degree Angle :A video showing how to construct a 15 degree angle with only a straightedge and compass.

How to Construct 60 Degree Angle :angle