How to Draw 45 degrees Angle?

We can construct a 45° angle,

• Using a Compass and Ruler
• Using Protractor

Construct a 45° Angle using a Compass and Ruler

To construct a 45° angle using compass and ruler, we can use the following steps:

Steps to Construct a 45°

Step 1: Draw a line segment: Start by drawing a straight line segment on your paper. Label the endpoints A and B.

Step 2: Create a right angle: With the compass point placed at point A, set the compass to any convenient radius. Draw an arc that intersects line segment AB at point C.

Step 3: Mark the intersecting points: Without changing the compass setting, place the compass point on point C and draw another arc that intersects the first arc above line segment AB. Label this intersection point D.

Step 4: Draw the perpendicular line: Now, use a ruler (optional) to draw a vertical line (perpendicular to line segment AB) passing through point D. Label the point where this line intersects line segment AB as E.

By drawing the intersecting arcs in steps 2 and 3, you’ve created a right angle (angle AEC) because any angle formed by the radius of a circle is a right angle.

Drawing 45-Degree Angle

• Bisect Right Angle: With the compass point on point D (the intersection point of the arcs) and the same compass setting used previously, draw another arc that intersects both the first arc (above line AB) and the vertical line drawn in step 4. Label this new intersection point F.

• Draw 45-Degree Angle: Finally, draw a line segment from point A to point F. This line segment creates angle FAB which is the 45-degree angle you wanted to draw.

Construct a 45° Angle using Protractor

Below is the step-by-step process describing how to draw a 45-degree angle using a protractor:

To construct a 45° angle using protector, we can use the following steps:

Steps to Construct a 45°

Step 1: Draw a line segment: Start by drawing a straight line segment on your paper. Label one endpoint A.

Step 2: Place the protractor: Align the centre of the protractor’s base (the straight edge without markings) exactly at point A on the line segment.

Step 3: Locate the 45-degree mark: Look for the markings along the outer edge of the protractor, which is typically a circular scale. Find the degree marking labelled “45” (or somewhere between 40 and 50 degrees).

Step 4: Mark the angle: Make a small pencil mark on the line segment at the point that aligns with the 45-degree mark on the protractor’s outer scale. Label this point B.

Step 5: Draw the angle: Finally, use a ruler (optional) to draw a straight line segment from point A to the point you marked in step 4 (point B). This line segment creates angle CAB, which is your 45-degree angle.

45-degree angle is a fundamental concept in geometry and trigonometry. An angle is a form of geometrical shape constructed by joining two rays to each other at their endpoints. The two lines joined together are called the arms of the angle.

A 45-degree angle is exactly half of a right angle, which measures 90 degrees. Two 45-degree angles placed together form a right angle. In degrees, a 45-degree angle is 45/360 of a complete circle since its measure is between 0 and 90 degrees, a 45-degree angle is classified as an acute angle.

In this article, we will learn about, a 45-degree angle, how to draw a 45-degree angle using a compass and protractor, the properties of a 45-degree angle trigonometric values of a 45-degree angle and others in detail.