7.G.5 Angles and Angle Relationships Today you will learn how to draw and classify angles.
An angle is made up of two rays with a common endpoint. Angles An angle is made up of two rays with a common endpoint. . A The point where the ends meet is called the vertex. . C . B
You can use the symbol for an angle, ,to name an angle. Naming Angles You can use the symbol for an angle, ,to name an angle. 1.Use the vertex as the middle letter and a point from each side. ABC or CBA . A 2. Use the vertex only. B 3. Use a number. 3 3 . C . B
Angles Angles are classified according to their measures. Angles are measured in units called degrees.
Acute angles are less than 90 degrees.
Right angles are exactly 90 degrees.
Obtuse angles are greater than 90 degrees, but less than 180 degrees.
Straight angles measure exactly 180 degrees.
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Classify the Angle Acute Obtuse Right Straight
Complementary Angles Two angle with a sum of 90˚
Supplementary Angles Two angle with a sum of 180˚
Complementary Supplementary Neither
Complementary Supplementary Neither Supplementary
Complementary Supplementary Neither
Complementary Supplementary Neither Supplementary
Complementary Supplementary Neither
Complementary Supplementary Neither
Complementary Supplementary Neither
Complementary Supplementary Neither
Complementary Supplementary Neither
Complementary Supplementary Neither
Protractors are used to measure angles. Measuring Angles Protractors are used to measure angles.
Measuring Angles To measure with the protractor, line up the vertex of the angle to the center of the hole at the middle bottom. Make one edge of the angle line up with where there would be a 0. Read on that scale where the other edge crosses.
Drawing Angles To draw a 75 degree angle, draw a ray with endpoint A. Place the center point of the protractor an A. Align the ray with 0 degrees. Use the scale that begins with 0 degrees. Locate the mark labeled 75 degrees. Draw the other side of the angle. A
Measure and classify the angle. Measuring Angles Measure and classify the angle. 110˚ , obtuse
Measure and classify the angle. Measuring Angles Measure and classify the angle. 70˚ , acute
Measure and classify the angle. Measuring Angles Measure and classify the angle. 70˚ , acute
Measure and classify the angle. Measuring Angles Measure and classify the angle. 178˚ , acute
Measure and classify the angle. Measuring Angles Measure and classify the angle. 120˚ , obtuse
Measure and classify the angle. Measuring Angles Measure and classify the angle. 15˚ , acute
Measure and classify the angle. Measuring Angles Measure and classify the angle. 30˚ , acute
Measure and classify the angle. Measuring Angles Measure and classify the angle. 90˚ , right
Measure and classify the angle. Measuring Angles Measure and classify the angle. 88˚ , acute
Measure and classify the angle. Measuring Angles Measure and classify the angle. 180˚ , straight
Adjacent angles share a common side.. Special Angles Adjacent angles share a common side.. ABC and CBD C . . D ABC and CBE CBD and BDE A . B . . E
Special Angles Vertical angles are congruent.
Adjacent Angles Angles that share a common side. 1 and 2 2 and 3 The adjacent angles formed by intersecting lines are supplementary angles.
Vertical Angles 1 and 3 2 and 4
Vertical Adjacent Neither
Vertical Adjacent Neither FAD and EAB Neither
Vertical Adjacent Neither COA and BOD Vertical
Vertical Adjacent Neither 1 and 3 Adjacent
Vertical Adjacent Neither
Vertical Adjacent Neither
Vertical Adjacent Neither 3 and 2 Vertical
Vertical Adjacent Neither ABD and KBC Neither
Vertical Adjacent Neither CAE and EAB Adjacent
Vertical Adjacent Neither ABD and DBK Adjacent
Vertical Adjacent Neither COB and BOD Adjacent
Vertical Adjacent Neither 1 and 4 Vertical
Vertical Adjacent Neither 1 and 5 Neither
Vertical Adjacent Neither 7 and 6 Vertical
Find the Missing Angles x = 104° y = 76° z = 104°
Find the Missing Angles 25° x = 155° y = 25° x z z = 155° y
Find the Missing Angles x x = 40° y = 40° 140° z z = 140° y
Find the Missing Angles COB = 110 ° 110° Find AOD AOD = 110 °
Find the Missing Angles COB = 110 ° 110° Find BOD BOD = 70 °
Find the Missing Angles 2 = 170 ° 170° Find 3 110° 3 = 170°
Find the Missing Angles 2 = 170 ° 170° Find 1 110° 1 = 10°
Find the Missing Angles x= 30° x 60
Transversal – a line that cuts through two or more lines Parallel lines- two lines running side by side but never touch. Transversal – a line that cuts through two or more lines
Alternate Interior Angles interior angles on opposite sides of the transversal. Alternate Interior Angles are Congruent 3 and 6 4 and 5
Alternate Exterior Angles – exterior angles on opposite sides of the transversal. Alternate Exterior Angles are Congruent 2 and 7 1 and 8
Corresponding Angles 2 and 6 4 and 8 1 and 5 1 and 8 Corresponding – angles in the same position of each line in relation to the transversal Corresponding Angles are Congruent 2 and 6 4 and 8 1 and 5 1 and 8
Find the Missing Angles 1 = 75 ° 2 = 105 ° 3 = 105 ° 4 = 75 ° 5 = 75 ° 6 = 105 ° 7 = 105 ° 8= 75 °