http://www.ck12.org Chapter 4. Triangles and Congruence
Vocabulary
Interior anglesare the angles on the inside of a polygon whileexterior anglesare the angles on the outside of a
polygon.Remote interior anglesare the two angles in a triangle that are not adjacent to the indicated exterior angle.
Two angles that make a straight line form alinear pairand thus add up to 180◦. TheTriangle Sum Theoremstates
that the three interior angles of any triangle will always add up to 180◦. TheExterior Angle Sum Theoremstates
that each set of exterior angles of a polygon add up to 360◦.
Guided Practice
- Findm^6 A.
- Findm^6 C.
- Find the value ofxand the measure of each angle.
Answers:
- Set up an equation using the Exterior Angle Theorem.m^6 A+ 79 ◦= 115 ◦. Therefore,m^6 A= 36 ◦.
- Using the Exterior Angle Theorem,m^6 C+ 16 ◦= 121 ◦. Subtracting 16◦from both sides,m^6 C= 105 ◦.
- Set up an equation using the Exterior Angle Theorem.
( 4 x+ 2 )◦+( 2 x− 9 )◦= ( 5 x+ 13 )◦
↑ ↗ ↑
interior angles exterior angle
( 6 x− 7 )◦= ( 5 x+ 13 )◦
x= 20 ◦Substituting 20◦back in forx, the two interior angles are( 4 ( 20 )+ 2 )◦= 82 ◦and( 2 ( 20 )− 9 )◦= 31 ◦. The exterior
angle is( 5 ( 20 )+ 13 )◦= 113 ◦. Double-checking our work, notice that 82◦+ 31 ◦= 113 ◦. If we had done the problem
incorrectly, this check would not have worked.
Practice
Determinem^6 1.
1.
2.
3.
4.
5.
6.Use the following picture for the next three problems:
- What ism^61 +m^62 +m^6 3?
- What ism^64 +m^65 +m^6 6?
- What ism^67 +m^68 +m^6 9?
Solve forx.