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Pairs of Angles Angles – sides and vertex angle This figure is called an _____. Some parts of angles have special names. S The common endpoint is called vertex the ______, and the two rays that make up the sides of the angle are called the sides of the angle. R vertex side T Naming Angles There are several ways to name this angle. 1) Use the vertex and a point from each side. SRT or S TRS The vertex letter is always in the middle. 2) Use the vertex only. R side R If there is only one angle at a vertex, then the angle can be named with that vertex. 3) Use a number. 1 1 vertex T Angles Review 1) Name the angle in four ways. ABC C A CBA B 1 1 B 2) Identify the vertex and sides of this angle. vertex: Point B sides: BA and BC Angle Classification Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle. Types of Angles A obtuse angle Greater than 90° A A right angle Equal to 90 ° acute angle Less than 90 ° Angle Classification Classify each angle as acute, obtuse, or right. 110° 40° 90° Obtuse Right Acute 50° 130° Acute Obtuse 75° Acute Straight Angles Opposite rays are two rays that are part of the ___________ same line and have only their endpoints in common. X Z Y opposite rays XY and XZ are ____________. The figure formed by opposite rays is also referred to as a ____________. straight angle A straight angle measures 180 degrees. Adjacent Angles When you “split” an angle, you create two angles. The two angles are called adjacent angles _____________ adjacent = next to, joining. B A 2 1 1 and 2 are examples of adjacent angles. They share a common ray. C Name the ray that 1 and 2 have in common. BD Adjacent Angles Determine whether 1 and 2 are adjacent angles. No. They have a common vertex B, but no common side _____________ 2 1 B 1 G Yes. They have the same vertex G and a common side with no interior points in common. 2 N J L 2 1 No. They do not have a common vertex or a____________ common side The side of 1 is LN The side of 2 is JN Complementary Angles Two angles are complementary if and only if The sum of their degree measure is 90. A E Definition of D Complementary Angles B 30° C 60° F mABC + mDEF = 30 + 60 = 90 Complementary Angles Some examples of complementary angles are shown below. 15° H P 75° mH + mI = 90 Q 40° mPHQ + mQHS = 90 50° H S U T I 60° V mTZU + mVZW = 90 30° Z W Supplementary Angles If the sum of the measure of two angles is 180, they form a special pair of angles called supplementary angles. Two angles are supplementary if and only if the sum of their degree measure is 180. Definition of Supplementary Angles D C 50° A 130° B E F mABC + mDEF = 50 + 130 = 180 Supplementary Angles Examples of supplementary angles are shown below. 75° H I mH + mI = 180 105° Q 130° 50° H P S U V 60° 120° 60° Z T mPHQ + mQHS = 180 mTZU + mUZV = 180 and mTZU + mVZW = 180 W Vertical Angles When two lines intersect, ____ four angles are formed. There are two pair of nonadjacent angles. These pairs are called _____________. vertical angles 4 1 3 2 Vertical Angles Two angles are vertical if and only if they are two nonadjacent angles formed by a pair of intersecting lines. Definition of Vertical angles: Vertical Angles 4 1 3 2 1 and 3 2 and 4 Vertical Angles Vertical angles are congruent. n 2 m 3 1 4 1 3 2 4 Vertical Angles Find the value of x in the figure: 130° x° The angles are vertical angles. So, the value of x is 130°.