Last modified on April 23rd, 2021

chapter outline

 

45 Degree Angle

What is a 45 Degree Angle

A 45 degree angle is an angle that measures 45 degree.

Figure 1 – Diagram (Heading: 45 Degree Angle, File name: 45 Degree Angle)

How to Make a 45 Degree Angle

Using a Compass

Replace letters A with X, Q with A, E with P, X with R, P with B, B with Y, F with Q, extended E with L,

Keep C, D and O same

Step 1: Draw a line OY of any length

Figure 2 – Diagram (File name –Making a 45 Degree Angle Using a Compass – Step 1)

Step 2: Now, take a compass and open it to any fixed radius.  With O as center, draw an arc that cuts the line segment OY at R

Figure 3 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 2)

Step 3: Again, using the compass, having the same radius, and with R as center, draw an arc at D

Figure 4 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 3)

Step 4: Using the compass, opened to the same radius, and with D as center, draw another arc at C

Figure 5 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 4)

Step 5: Again, using the compass with the same radius, and with C and D as center draw two arcs which cuts each other at P

Figure 6 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 5)

Step 6: Join line OP using a ruler and extend it to X. The angle formed∠XOY = 90°

Figure 7 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 6)

Now, to draw a 45 degree angle, we need to draw an angle bisector of ∠XOY

Step 7: Again using compass with any convenient radius, and with O as center, draw an arc that cuts line OY at B and OX at A

Figure 8 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 7)

Step 8: Again using compass, opened to the same radius, and with A and B as centers, draw two arcs that cuts each other at point Q

Figure 9 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 8)

Step 9: Join OQ and extend it to L

Figure 10 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 9)

Step 10: OL is the bisector of ∠XOY. The two angles formed ∠XOL and ∠LOY measures 45° each, such that ∠ XOL + ∠LOY = 90°

Cutting a 45° Angle

Figure 11 – Diagram (File name – Making a 45 Degree Angle Using a Compass – Step 10)

Figure 12 – Diagram (Heading: How to Make a 45 Degree Angle Using a Compass, File name – How to Cut a 45 Degree Angle)

Make a collage of all the steps from step 1 to step 10

Using a Protractor

Step 1: Draw a ray and name it AB

Figure 13 – Diagram (File name –Making a 45 Degree Angle Using a Protractor – Step 1)

Step 2: Keep the center of the protractor at A

Step 3: Using the outer circle of the protractor look or 45° and mark a point C over it

Figure 14 – Diagram (File name – Making a 45 Degree Angle Using a Protractor – Step 2)

Mark points A, B, C

Step 4: Join OC

The angle formed∠COB measure 45°

Figure 15 – Diagram (Heading: How to Make a 45 Degree Angle Using a Protractor, File name – How to Make a 45 Degree Angle)

Make a collage of all the steps from step 1 and 2

How to Measure a 45 Degree Angle

To measure and say whether the given angle is 45°, use a protractor and follow the following steps:

Step 1:

The protractor is aligned with the given ray OX as shown below.

Figure 16 – Diagram (file name: Measuring a 45 Degree Angle –Step 1)

The reading is initiated from the 0 mark on the bottom right of the protractor.

Step 2:

The number on the protractor that coincides with the second ray OY, is the measure of the given angle.

Figure 17 – Diagram (file name: Measuring a 45 Degree Angle –Step 2)

The value recorded using the number on the lower arc of the protractor is 45°.

Figure 18 – Diagram (Heading: How to Measure a 45 Degree Angle, File name – How to Measure a 45 Degree Angle)

Make a collage of all the steps from step 1 and 2

Examples in Real Life

  • The solar panels inclined towards the sun to trap sunlight
  • Used in architecture to construct designer doors and window grills

E.g 1) Krish drew a horizontal line on a piece of paper. Kriti divided it into two equal halves by drawing a vertical line over it. Kiran further divided the two parts into four equal parts. Finally, their drawing is given below. How many 45 degrees are there?

Diagram (File name – 45 degree Angle – Question 1)

Krish divided the horizontal line to get two angles measuring 90° each. Kriti further divided each of the right angles to get four 45° angle as shown below.

So totally there are four 45° angles in the straight line drawn by Krish.

Diagram (File name – 45 degree Angle – Answer 1)

Last modified on April 23rd, 2021

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