We will determine1 the measures of Interior and Exterior Angles. LEARNING OBJECTIVE Definition 1 figure out Declare the Objective A read the objective to B

ACTIVATE PRIOR KNOWLEDGE Given and , find each measure next to the appropriate angle to show the correct measure for each angle. Remember the Concept Supplementary angles are two angles with a sum of 180∘  Triangle Sum Theorem The sum of the three interior angles in a triangle is always 180 2 Find: ACTIVATE PRIOR KNOWLEDGE 1 Find: 55 Make the Connection Students, you already know how apply triangle sum theorem. Today, we will learn how to find the missing measurements of Interior and Exterior Angles.

Example Check for Understanding What is exterior Angle Theorem? CONCEPT DEVELOPMENT Check for Understanding What is exterior Angle Theorem?

1. 2. How do you find the angle H? Apply the remote interior angles. CONCEPT DEVELOPMENT Apply the remote interior angles. Apply the remote interior angles. Check for Understanding How do you find the angle H?

SKILL DEVELOPMENT / GUIDED PRACTICE 1 Identify what is given and what you are solving for. 2 Apply the appropriate theorem(s). 3 Solve and check your solution 1. Determine the measure of the indicated exterior angle in the diagram. 2. Determine the measure of the indicated exterior angle in the diagram Remember the Concept Triangle Sum Theorem The sum of the three interior angles in a triangle is always 180. Supplementary angles are two angles with a sum of 180. Exterior Angle Theorem - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle. Triangle Sum Theorem = 180 Supplementary angles SKILL DEVELOPMENT / GUIDED PRACTICE 70 + = 180 180 - = 180-70 = 110 Check for Understanding How do you find the missing angle?

SKILL DEVELOPMENT / GUIDED PRACTICE 1 Identify what is given and what you are solving for. 2 Apply the appropriate theorem(s). 3 Solve and check your solution 1. Find the angle measure 2. Remember the Concept Triangle Sum Theorem The sum of the three interior angles in a triangle is always 180. Supplementary angles are two angles with a sum of 180. Exterior Angle Theorem - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle. Same SKILL DEVELOPMENT / GUIDED PRACTICE 2( ) + = 180 Check for Understanding How do you find the missing angle?

16– 12c= 0 -16 -16 4 – 4(3)(c) = 0 – 12c= -16 -12 -12 16– 12c= 0 Find the c: Solve for c: = 0 16– 12c= 0 -16 -16 4 – 4(3)(c) = 0 2 – 12c= -16 -12 -12 16– 12c= 0 c = 3/4

A ladder propped up against a house makes a 25° angle with the wall A ladder propped up against a house makes a 25° angle with the wall. What would be the ladder's angle measure with the ground facing away from the house? The house is perpendicular to the ground, so the other remote interior angle is 90°. The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. RELEVANCE Check for Understanding Does anyone else have another reason why it is relevant to use the measures of Interior and Exterior Angles Write and solve an equation relating the exterior and remote interior angles. 25 + 90 = 115 So, the measure of the indicated exterior angle is 115°.

What did you learn today about determining the measures of Interior and Exterior Angles. Word Bank Exterior Angle Theorem Triangle Sum Theorem Supplementary angles  SUMMARY CLOSURE