45 Degree Angle

A 45-degree angle is an acute angle. It is half of the right angle or 90-degree angle. An angle bisector of a 90-degree angle forms two equal angles of 45 degrees each. The 45-degree angle can be seen in so many places in our day-to-day life, such as in scissors, doors, windows, etc. It is also seen as the angle formed by the diagonal of a square with its sides.

A 45-degree angle is exactly half of a 90-degree angle formed between two rays. It is an acute angle and two angles measuring 45 degrees form a right angle or a 90-degree angle. We know that an angle is formed when two rays meet at a vertex. Look at an image of a 45-degree angle below.

If the angle formed at the vertex O measures 45 degrees, we call it a 45-degree angle.

We can easily construct a 45-degree angle with or without a protractor. It can be drawn with the help of a ruler and compass as well. Let us learn the methods to draw a 45-degree angle one by one.

Construction of 45-Degree Angle Using a Protractor

Constructing a 45-degree angle using a protractor is an easy process. We can draw a 45-degree angle by using the following steps:

• Step 1: Draw a line segment OB.
• Step 2: Place the protractor at point O.
• Step 3: In the outer circle of the protractor, look for 45 degrees reading, and with a pencil mark a dot and name it A.
• Step 4: Join O and A now. Angle ∠AOB = 45°.

Constructing 45 Degree Angle with a Compass

To understand how to construct a 45-degree angle using a compass, follow the steps given below:

• Step 1: Draw a horizontal ray BD (as shown in the figure below).
• Step 2: Take any suitable width on the compass which is generally more than half of BD and draw an arc by keeping the compass tip at point B, which will intersect BD at point C.
• Step 3: Without changing the width of the compass, place the compass tip at point C and cut the arc drawn in step 2. Name that point as P.
• Step 4: Keep the compass tip at point P (without any change in the width of the compass), and cut the arc drawn in step 2. Name that point as Q.
• Step 5: By keeping the compass tip at P, draw an arc between P and Q which will lie above point B. Intersect this arc by another arc drawn from point Q. Name this point as A.
• Step 6: Join B to A. This will be a 90-degree angle. Now we just have to draw an angle bisector of the 90-degree angle to get a 45-degree angle. Place the compass tip at point C and draw an arc anywhere inside the angle ABD.
• Step 7: Now place the compass tip at point A and cut the arc drawn in step 6. Mark that point as E. Join B to E. Angle EBD is the required angle of 45 degrees.

This is how we can construct an angle of 45 degrees with a compass and a ruler.

We can see the 45-degree angle in so many places around us, for example, the laptop lid will make a 45-degree angle with its base if kept appropriately, doors make a 45-degree angle if held properly. Angles are all around us when you open your mouth also our lips form an angle. Observe where you can see 45-degree angles in your surrounding areas.

Let us see a few examples of 45-degree angles in our surroundings:

• A 45-degree angle is the best angle for the sun's rays to reach the farthest distance. This is why some solar panels are inclined to 45 degrees based on geographical position.
• Also when you want to throw a ball, a 45-degree angle is the best as it reaches the farthest, you will read this in physics in coming years in depth.
• A 45-degree angle is used in architecture to construct designer doors and window grills.

Topics Related

Check out some interesting topics related to a 45-degree angle.

• 60 Degree Angle
• 30 Degree Angle
• 180 Degree Angle
• 270 Degree Angle

What does a 45-Degree Angle Look Like?

45-degree angle looks like a greater than (>) sign or lesser than sign (<). If we draw an angle bisector to a 90-degree angle, the small angles thus formed will be 45-degree angles. It also looks like the open face of scissors.

What is the Complement of a 45 Degree Angle?

The complement of an angle is the measurement of an angle that is needed to be added to the given angle to make the sum 90 degrees. The complement of 45-degree angle can be calculated as 90° - 45° = 45 degrees.

What is Half of a 45 Degree Angle?

The half of a 45-degree angle is 45/2 = 22.5 degree angle. It can be constructed by drawing an angle bisector of a 45-degree angle.

How to Draw 45 Degree Angle with Compass?

To draw a 45-degree angle with a compass, we first construct a 90-degree angle. Then we construct an angle bisector of 90 degrees to get a 45-degree angle.

How Many 45 Degree Angles does it take to make a Full Turn?

A full turn is 360°. Since 45 × 8 = 360, there are eight 45° in a full turn.

How to Measure 45 Degree Angle?

We can measure the 45-degree angle using a protractor. We align the base of the angle with the straight line at the protractor. Align the center of the protractor with the vertex of the angle, then check the other arm of the angle if it aligns with the 45-degree line of the protractor or not.