How To Draw 75 Degree Angle With Compass

Constructing a 60° angle

This folio shows how to construct (draw) a lx degree angle with compass and straightedge or ruler. This construction works by creating an equilateral triangle. Recollect that an equilateral triangle has all three interior angles 60°. We utilise ane of those angles to get the desired threescore degree result. See the proof below for more details.

Printable stride-by-step instructions

The above animation is available as a printable pace-by-footstep educational activity canvas, which can be used for making handouts or when a reckoner is not available.

Proof

This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all iii interior angles 60°. The image below is the terminal drawing above with the red items added.

	Argument	Reason
1	Line segments AB, Lead, PA are congruent	All drawn with the same compass width.
2	Triangle APB is an equilateral triangle	Equilateral triangles are those with all iii sides the same length.
3	Angle APB has a measure of 60°	All three interior angles of an equilateral triangle have a measure of sixty°. Come across Equilateral triangle definition

- Q.E.D

Try information technology yourself

Click here for a printable worksheet containing ii 60° angle exercises. When you get to the page, use the browser print control to print every bit many every bit you wish. The printed output is non copyright.

Other constructions pages on this site

List of printable constructions worksheets

Lines

Introduction to constructions
Copy a line segment
Sum of n line segments
Difference of 2 line segments
Perpendicular bisector of a line segment
Perpendicular at a signal on a line
Perpendicular from a line through a signal
Perpendicular from endpoint of a ray
Separate a segment into north equal parts
Parallel line through a point (angle re-create)
Parallel line through a point (rhomb)
Parallel line through a point (translation)

Angles

Bisecting an angle
Re-create an angle
Construct a 30° angle
Construct a 45° angle
Construct a 60° angle
Construct a 90° angle (correct angle)
Sum of n angles
Departure of 2 angles
Supplementary angle
Complementary angle
Constructing 75° 105° 120° 135° 150° angles and more than

Triangles

Copy a triangle
Isosceles triangle, given base and side
Isosceles triangle, given base and altitude
Isosceles triangle, given leg and apex angle
Equilateral triangle
30-60-90 triangle, given the hypotenuse
Triangle, given iii sides (sss)
Triangle, given one side and next angles (asa)
Triangle, given ii angles and non-included side (aas)
Triangle, given two sides and included angle (sas)
Triangle medians
Triangle midsegment
Triangle distance
Triangle altitude (outside case)

Right triangles

Right Triangle, given i leg and hypotenuse (HL)
Right Triangle, given both legs (LL)
Right Triangle, given hypotenuse and 1 angle (HA)
Right Triangle, given one leg and i angle (LA)

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the center of a circle
Circle given 3 points
Tangent at a point on the circle
Tangents through an external point
Tangents to two circles (external)
Tangents to 2 circles (internal)
Incircle of a triangle
Focus points of a given ellipse
Circumcircle of a triangle

Polygons

Foursquare given one side
Square inscribed in a circumvolve
Hexagon given one side
Hexagon inscribed in a given circumvolve
Pentagon inscribed in a given circumvolve

Not-Euclidean constructions

Construct an ellipse with string and pins
Find the heart of a circumvolve with whatever correct-angled object

Source: https://www.mathopenref.com/constangle60.html

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