Table of Contents

Last modified on April 23rd, 2021

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

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

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**

**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**

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**

- 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