Use a protractor to draw angles with the following measurements: Warm Up Use a protractor to draw angles with the following measurements: 48⁰ 110⁰ 5⁰ 175⁰

Combining Angles

Congruent Angles = = STV PQR STV m PQR 100⁰ Congruent angles – have the same measure. PQR STV Example: or PQR m STV = = 100⁰

Angle Addition Postulate Angle Bisector An angle bisector is a ray that divides one angle into two congruent angles Ray YW bisects XYZ

Example – Angle Addition Postulate = 2(23) + 10 = 46 + 10 = 56⁰ = 4x - 3 + = 145⁰ = 4(23) - 3 (2x + 10) + (4x – 3) = 145⁰ = 92 - 3 = 89⁰ 6x + 7 = 145 Combine like terms 6x = 138 Subtract 7 from both sides x = 23 Divide both sides by 6

Angle Pairs Complementary angles – two angles whose measures add up to 90⁰ Supplementary angles – two angles whose measures add up to 180⁰ Adjacent angles – two angles that share a common vertex and side

More Angle Pairs Vertical angles – sides form two pairs of opposite rays Linear Pairs– two angles are a linear pair when their non- common sides are opposite rays non - common side non - common side

Draw two congruent angles (any kind). Label the measure. Whiteboard Activity Draw an acute angle labeled ABC Draw two adjacent angles Draw two adjacent angles that are complimentary Draw one angle and label the vertex and sides. Draw an obtuse angle labeled JKL Draw a straight angle. Draw a right angle labeled XYZ Then draw a ray YW that is a bisector of that angle.