4.2: Angle Relationships in Triangles Objectives: Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles. Supplies: Math Notebook Textbook Assignment: p. 228 #15-23(skip 17), 29-32

4.2: Angle Relationships in Triangles A line drawn connected to a shape to help write a proof. In this case I have extended a side of a triangle to create an exterior angle. An angle on the inside of a shape. An angle that is created by extending a side of a shape. (in this picture, and the next, it is the angle mark in black) The two angles not connected to the created exterior angle. Another way to say this is that they are the angles opposite the exterior angle. (In the picture the turquoise and purple angles.)

4.2: Angle Relationships in Triangles ∠A+∠B+∠C=180° ∠A+∠B=∠D If ∠A=∠E and ∠B=∠F then ∠C=∠G Corollaries to Triangle Sum Theorem 4-2-2: The acute angles of a right triangle are complementary. 4-2-3: If a triangle is equiangular, then each angle measures 60°. H K ∠H + ∠K=90°

4.2: Angle Relationships in Triangles After an accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find mXYZ. Sum. Thm mXYZ + mYZX + mZXY = 180° mXYZ + 40 + 62 = 180 Substitute Property mXYZ + 102 = 180 Simplify. mXYZ = 78° Subtract 102 from both sides.

4.2: Angle Relationships in Triangles After an accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find mYWZ. 180-(62+40)=180-102=87 180- (40+(12+87))=180-(40+99)=180-139=74 I just solved it! Can you rewrite my work in proof form and provide justification for each step? 1 Bonus point on the next quiz if you can and do.

4.2: Angle Relationships in Triangles The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle? Statement Proof ∠A+∠B=90° Acute angles of a right triangle are complementary ∠A+∠63.7° =90° Substitution property ∠A =26.3° Subtraction property of equality The measure of one of the acute angles in a right triangle is 48  . What is the measure of the other acute angle? 90°-48 °=42 If I asked you to write a proof and give you space on a quiz. Which one of these answers would get all 6 points? How many points would you give someone for the other answer?

4.2: Angle Relationships in Triangles Find mB. Given Justification m∠A+m∠B= m∠BCD Exterior Angles Theorem 15+2x+3= 5x-60 Substitution property 2x+18= 5x-60 Simplification 78=3x Subtraction property of equality 26=x Division property of equality m∠B= 2x+3 Given m∠B= 2(26)+3 Substitution m∠B= 55° Simplification.

4.2: Angle Relationships in Triangles Find mACD. Statement Justification m∠ABC +m∠BAC =m∠ACD 90°+(2z+1)°=(6z-9)° 2z+91=6z-9 100=4z 25=z m∠ACD=(6z-9) m∠ACD=6(25)-9 m∠ACD=141° I provided the statements, If You provide justifications for each step, Then you will receive 1 Bonus point on the next quiz.

4.2: Angle Relationships in Triangles Find mK and mJ. Statement Justification m∠FKH= m∠IJG Third angles theorem 4y²=6y²-40 Substitution property 40=2y² Subtraction property of equality 20= y² Division property of equality m∠FKH=4y² Given m∠FKH=4(20) Substitution m∠FKH=80 Simplification m∠IJG=80 Transitive property of equality

4.2: Angle Relationships in Triangles Assignment: p. 228: 15-23(skip 17), 29-32