# MEASURING ANGLES

To measure an angle, we must need the following mathematical instrument.

Protractor

Let us see how an angle can be measured using protractor through the following examples step by step.

Example 1 :

Measure the angle given below. Important Note :

In the figure given above, the vertex of the angle is found on the left side.

Whenever we measure angle where its vertex is found on the left side, we have to consider the angles on the bottom row of the protractor.   .

In case, the vertex of the angle is found on the right side, we have have to consider the angles on the top row of the protractor.

Step 1 :

Place the midpoint of the protractor on the vertex (at P) of the angle.

Step 2 :

Line up one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

Step 3 :

In the above figure, since the vertex of the angle is found on the left side, we have to consider the angles on the bottom row of the protractor

Step 4 :

Read the degrees on the bottom line of the protractor where the other side (PQ) crosses. In the above figure, one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

The other side of the angle (PQ) crosses at 60° on the bottom row of the protractor.

So, measure of the given angle is 60°.

Example 2 :

Measure the angle given below. Step 1 :

Place the midpoint of the protractor on the vertex (at P) of the angle.

Step 2 :

Line up one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

Step 3 :

In the above figure, since the vertex of the angle is found on the left side, we have to consider the angles on the bottom row of the protractor

Step 4 :

Read the degrees on the bottom line of the protractor where the other side (PQ) crosses. In the above figure, one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

The other side of the angle (PQ) crosses at 125° on the bottom row of the protractor.

So, measure of the given angle is 125°.

Example 3 :

Measure the angle given below. Step 1 :

Place the midpoint of the protractor on the vertex (at P) of the angle.

Step 2 :

Line up one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

Step 3 :

In the above figure, since the vertex of the angle is found on the right side, we have to consider the angles on the top row of the protractor

Step 4 :

Read the degrees on the top line of the protractor where the other side (PQ) crosses. In the above figure, one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

The other side of the angle (PQ) crosses at 75° on the top row of the protractor.

So, measure of the given angle is 75°.

Example 4 :

Measure the angle given below. Step 1 :

Place the midpoint of the protractor on the vertex (at P) of the angle.

Step 2 :

Line up one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

Step 3 :

In the above figure, since the vertex of the angle is found on the right side, we have to consider the angles on the top row of the protractor

Step 4 :

Read the degrees on the top line of the protractor where the other side (PQ) crosses. In the above figure, one side of the angle (PA) with the zero line of the protractor (where you see the number 0).

The other side of the angle (PQ) crosses at 144° on the top row of the protractor.

So, measure of the given angle is 144°.

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