Construction of special angles — lesson. Mathematics State Board, Class 7.

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In this lesson, let us construct some special angles by without using the protractor.

i) Construction of

$60°$ angle:

Step 1: First draw a straight line, and mark a point

$A$ on it.

Step 2: Take the point

$A$ as centre, draw an arc of convenient radius to the line to meet at a point

$B$ .

Step 3: With the same radius, take

$B$ as centre, draw an arc to cut the previous arc at

$C$ .

Step 4: Join

$AC$ . Then

$∠BAC$ is the required angle with the measure

$60°$ .

ii) Construction of

$135°$ angle:

Step 1: First draw a straight line, and mark a point

$A$ on it.

Step 2: Take the point

$A$ as centre, draw an arc as below which meet at a point

$B$ .

Step 3: Take radius, and draw an arc for

$60°$ , as shown above. This cuts an arc at point

$C$ .

Step 4: Now take

$C$ as centre, draw an arc to with the same radius, point it as

$D$ . Here the point

$D$ gives the angles of

$120°$ .

Step 5: With the same radius, draw an arc from the point

$D$ that cuts the

$E$ which gives the

$180°$ .

Step 6: Finally, draw the angle bisector between the two points

$D$

$(120°)$ and

$E$

$(180)$ . The angle bisector separates the two points

$D$ and

$E$ and gives the angle

$150°$ . Now again find the angle bisector between

$150°$ and

$120°$ , the resultant gives the required angle

$135°$ .

The measure of

$135°$ angle, can be drawn in many ways, without using the protractor. Refer the below video for further information and clarification to construct the

$135°$ angle.

Construct

$135°$ degree using ruler and compass:

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9. Construction of special angles

Theory: