Properties of 45-degree Angle

The most important property of a 45-degree angle is its measure about a right angle:

• Half of a right angle: A 45-degree angle is exactly half of a right angle which measures 90 degrees. This means two 45-degree angles placed together form a right angle.

Other Properties

• Special right triangle: When a right triangle has one angle measuring 90 degrees and the other two angles are congruent (equal), those other two angles each measure 45 degrees. This type of right triangle is called a 45-45-90 triangle.

• Side ratios in a 45-45-90 triangle: In a 45-45-90 triangle, the length of the hypotenuse (the side opposite the right angle) is 2​ times the length of either of the legs (the two sides forming the right angle).

• Unit circle: A 45-degree angle corresponds to a specific point on the unit circle in trigonometry. This point is where the x and y coordinates are each equal to 1/√2.
• Square diagonals: The diagonals of a square create two 45-degree angles with each of the square’s sides.

While not a property of the angle itself, a 45-degree angle is also:

• Classified as an acute angle because its measure is between 0 and 90 degrees.

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.