LINES AND ANGLES

5. TYPES OF ANGLES

You must know several types of angles as follows.

1. Right Angle, i.e. an angle with the measure of 90 degrees.

Here these figure!

figure 1.Right Angle with its measure 90 degrees.

figure 2. Right Angle with its symbol.

you  can watch this VIDEO for  right angle.
http://go.webvideoplayer.com/webvideo.player?d0qMD2URzX6ONBCaFIWe

2. Acute angle, i.e.an angle with the measure is less than 90 degrees.

Here these figures.

figure 3. Area of Acute Angle.

figure 4. Every  acute angle always less than 90 degrees.

You can watch this video.

http://go.webvideoplayer.com/webvideo.player?Uz61gdumVZwYIvJb7Wao

3. Obtuse Angle,i.e. an angle with the measure is greater than 90 degrees but less than 180 degrees.

Here these figures.

figure 5. Obtuse angle with measure more than 90 degrees but less than 180 degrees.

figure 6. Each obtuse angle always be more than 90 and less than 180 degrees.

You may see this VIDEO.

http://go.webvideoplayer.com/webvideo.player?VEqgdv59lJPQYXcbwh47

4. Straight Angle, i.e. an angle with the measure 0f 180 degrees.

Here this figure.

figure 7. Straight  Lines.

You may see this video.

http://go.webvideoplayer.com/webvideo.player?P5hk6lwp1d8S3iZLKnjq

5. Reflex  angle,i.e. an angle with the measure is greater than 180 degrees.

Here these figures.

figure 8. Each reflex angles always more than 180 degrees.

figure 9. Reflex angle with measure 248 degrees.

figure 10. Reflex angle with measure 311 degrees.

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LINES AND ANGLES

Februari 16, 2012

4.DRAWING AND MEASURING THE ANGLES

We can measure an angle using protractor. You can see the protractor as the following picture.

Now, consider how to measure an angle by using protractor.

1. Consider the following .

2. Place the protractor on . Th e center of the protractor coincides with O and the horizontal line of the protractor coincides with OC as the picture in the following.

3. The picture above shows that  coincides with number 130 degrees (outer scale) and 60 degrees (inner scale). The measure of  is 130 degrees because it is measured by using inner scale.

You can watch this video to know how measure an angle that less than 180 degrees.
http://go.webvideoplayer.com/webvideo.player?0jZSV2TBNpkdweY96IKW

You also can watch this video to measure an angle more than 180 degrees.

http://go.webvideoplayer.com/webvideo.player?rymZEKQGef7WO9P1DjBX

DRAWING ANGLES WITH A PROTRACTOR

To draw an angle with a protractor, proceed as follows: Draw a straight line (i.e. an arm of the angle). Place a dot at one end of the arm.  This dot represents the vertex of the angle. Place the centre of the protractor at the vertex dot and the baseline of the protractor along the arm of the angle. Find the required angle on the scale and then mark a small dot at the edge of the protractor. Join the small dot to the vertex with a ruler to form the second arm of the angle. Label the angle with capital letters. EXAMPLE 1 SOLUTION: Draw a straight line AB. Place a dot at B.  This dot represents the vertex of the angle. Place the centre of the protractor at B and the baseline of the protractor along the arm BA. Find 60º on the scale and mark a small dot at the edge of the protractor. Join the vertex B to the small dot with a ruler to form the second arm, BC, of the angle. Mark the angle with a small arc as shown below. DRAWING REFLEX ANGLES To draw a reflex angle (i.e. angle greater than 180º and less than 360º), proceed as follows: Subtract the reflex angle from 360º.  Then draw the resulting angle as described earlier. The required angle is outside the one that has been drawn. Mark the angle with a small arc. Label the angle. EXAMPLE 2 SOLUTION: Draw a straight line PQ. Place a dot at Q.  This dot represents the vertex of the angle. Turn the protractor upside down and place the centre of the protractor at Q and the baseline of the protractor along the arm PQ. Use the outer scale to find 120º and mark a small dot at the edge of the protractor. Then remove the protractor and join the vertex, Q, to the small dot with a ruler to form the second arm, QR, of the angle. Mark the angle with a small arc as shown below.