What is the definition for angle addition postulate for the measure of an angle? This is from a geometry pre-test vocabulary worksheet. I am in 9th grade geometry.

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hustoncmk | High School Teacher | (Level 1) Assistant Educator

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The angle addition postulate states that if a point is within an angle and you add the two angles that are made by drawing a line through the point that the total will equal the large angle.  For example, point D lies in the middle of angle ABC, the angles ABD and CDB will add up to angle ABC.

An angle can be measured in degrees or radians. The definition for meausre of an angle accoriding to http://mathopenref.com is 

Measure of an angle

In geometry an angle is measured in degrees, where a full circle is 360 degrees. As in the figure above, a smallish angle might be around 30 degrees. For very small angles, the degree is further divided in to 60 minutes. For even smaller measurements the minute is divided again into 60 seconds, However this last measure is so small, it only used where angles are subtended over extreme distances such as astronomical measurements, and measuring latitude and longitude.

    

Measure of an angle

In geometry an angle is measured in degrees, where a full circle is 360 degrees. As in the figure above, a smallish angle might be around 30 degrees. For very small angles, the degree is further divided in to 60 minutes. For even smaller measurements the minute is divided again into 60 seconds, However this last measure is so small, it only used where angles are subtended over extreme distances such as astronomical measurements, and measuring latitude and longitude.

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neela | High School Teacher | (Level 3) Valedictorian

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Let O be the centre of the circle , OX be the initial line, Let OB be variable line with O at the centre and B on the circumference of the circle.

Then for any position B on the circle, measure of angle XOB =  measure of the mutual inclinatof OX and OB at O = The measure of the distance XB along the circumference/ The radius of the circle OX. This type of measure of angle is called radian.

The one full round of angle along the cirlce = angle XOB , when B moves alon the circumference and coincides first time with x = one distance equal to the cicumference/ radius = 2pi. If  2pi  is diveded  360 parts , then each part is called a degee of measure of the angle.

Addition postulate of angle: If   PQR and RQS, (where QP , QR, QS  the the rays with common vertex Q)   are two angles, then

measure of angle PQR + measure of angle RQS = measure of angle PQS.

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