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Section 1-4: Angles A. Angle: Formed by two rays with a common endpoint. Diagram of an angle. W Z interior X exterior XW and Y are the sides of an angle Sides of an angle are formed by two rays. XY X is the vertex because it is the common endpoint. *An angle separates a plane in 3 distinct parts: 1. Interior of the angle. 2. Exterior of the angle. 3. Angle itself. B. Measuring Angles: 1. Protractor: Tool that measures angles measured in degrees. 2. Types of Angles: a. A is a right angle if mA is 900 A b. A is an acute angle if mA is less than 900 c. A A is an obtuse angle if mA is more than 900 and less than 1800 d. A is a straight angle if mA is 1800. 3. A A Other Types of Angles: a. Congruent Angles: angles that have equal measure Angle measures are equal, but the angles are congruent Ex: m 5 = m 6 *m in front of an angle 5 6 means the measure of the angle P R 5 Q b. R Q S Adjacent Angles: Two angles in a plane that have a common vertex and a common side, but no common interior points. P 5 6 6 S Since 5 and 6 share a common side, Q R , and a common vertex, Q, 5 and 6 are adjacent angles. c. Bisector of an Angle: The ray that divides the angle into two congruent adjacent angles. QR If bisects PQS , then m 5 = m 6 or 5 6 P R 5 Q 6 S If m 5 = m 6 , then bisects PQS . QR C. When naming an angle… a. The vertex must be in the middle when using 3 points Ex: PQS understood Q is the vertex b. You may name it by its vertex only if it names exactly one angle D. Angle Addition Postulate ~ If R lies in the interior of PQS then MPQR MRQS MPQS ~ If MPQR MRQS MPQS then R is in the interior of PQS