Date: Topic: Types of Angles (6-2) An angle is the union of two rays with a common endpoint. The endpoint is the vertex of the angle, and each ray is a.

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Presentation transcript:

Date: Topic: Types of Angles (6-2) An angle is the union of two rays with a common endpoint. The endpoint is the vertex of the angle, and each ray is a side of the angle. P Q angle QPR angle RPQ Postulate 7 Protractor Postulate: The measure of angle can be calculated by the absolute value of the rays degree measures: m stands for measure R 1 angle P angle 1

Types of Angles equal to 180˚Straight greater than 90˚and less than 180˚Obtuse equal to 90˚Right greater than 0˚and less than 90˚Acute ExampleMeasureType of Angle O Q R B A

interior angle Two angles are complementary if the sum of their measures is 90˚ An angle with measure less than 180˚, divides the plane in three sets of point. The angle itself in the interior of the angle, and the points in the exterior of the angle. P Q R exterior angle Two angles are supplementary if the sum of their measures is 180˚ J39˚ K 51˚ 39˚ + 51˚ = 90˚ G 47˚ H 133˚ 47˚ + 133˚ = 180˚

Postulate 8 Angle Addition Postulate: If point B lies in the interior of then: If is a straight angle, and B is any point not on, then: O B C A O B AC

When complementary angles are adjacent, the exterior sides form a right angle. Adjacent angles are two angles in the same plane that share a common side and a common vertex, but have no interior points in common. When supplementary angles are adjacent, the exterior sides form a straight angle. B D AC 47˚133˚ Q S R T 39˚ 51˚

Solve for a: adjacent complementary angles form a right angle (90˚) Y V U W a˚ (a+42)˚ substitute values combine like terms subtract 42 to both sides 2 2 divide both sides by 2

+ 15 º +15 º º - 10 º 2 2