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# Angle and its measurement ## Let's Study * Directed angle * Angles of different measurements * Units of measure of an angle * Length of an arc of a circle * Area of a sector of a circle ## Let's Recall * We know how to draw the acute angles of different measures. * In a circle, we can find arc...

# Angle and its measurement ## Let's Study * Directed angle * Angles of different measurements * Units of measure of an angle * Length of an arc of a circle * Area of a sector of a circle ## Let's Recall * We know how to draw the acute angles of different measures. * In a circle, we can find arc length and area of a sector in terms of the central angle and the radius. ## Activity No. 1 * Draw the angle ABC of measure 40° ## Let's Learn ### 1.1 Directed Angles: * Consider the ray OA. Rotate it about O till it takes the position OB as shown in Fig. 1.3. Then the angle so obtained due to the rotation is called directed angle AOB. We define the notion of directed angle as follows: ### Definition: * The ordered pair of rays (OA, OB) together with the rotation of the ray OA to the position of the ray OB is called the directed angle ∠AOB. * If the rotation of the initial ray is anticlockwise then the measure of directed angle is considered as positive, and if it is clockwise then the measure of the directed angle is considered as negative. In the ordered pair (OA, OB), the ray OA is called the initial arm and the ray OB is called the terminal arm. * In Fig. 1.1 and 1.2 both the angles are of 40°. But one is measured in anticlockwise direction and the other is measured in clockwise direction.