Angle Relationships with Complementary and Supplementary Angles.

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Presentation transcript:

Angle Relationships with Complementary and Supplementary Angles

K J A ray is a part of a line that starts at one point and extends forever in one direction. KJ K J Parallel lines are two lines that never cross M N A M Perpendicular lines are two lines that form a 90 0 angle. T H Quick review not in notes

An angle () is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees. m1 means the measure of 1. The angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter. X Y Z 1 m1 = 50° Quick review not in notes

The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°. E F K J G H A right angle measures 90°. An acute angle measures less than 90°. An obtuse angle measures greater than 90° and less than 180°. Complementary angles have measures that add to 90°. Supplementary angles have measures that add to 180°.

EX1) Name the angle. TQS SQTQQ right EX2) Name the angle.... T Q S... Z J K ZJK KJZJJ acute... V B H EX3) Name the angle. VBH HBVBB obtuse EX4) Name the angle. FMN NMFMM straight... FMN 1 22 33 44

Vertical Angles Adjacent Angles - Opposite Angles - Touching Angles. Common vertex and side. No overlap 11& 3 22& 4 11& 2 33 & 4 11 22 & 3

EX 7) Find X 75 ○ (2x + 15) ○ We know these angles are vertical so they are congruent ( ) 2x + 15 = x = x = 30

EX4) Name a pair of complementary angles. TQP, RQSmTQP + mRQS = 47° + 43° = 90° EX5) Name two pairs of supplementary angles. TQP, RQT SQP, SQR mTQP + mRQT = 47° + 133° = 180° mSQP + mSQR = 137° + 43° = 180°

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