1. 4.2 Angles of Triangles

2. Objectives Apply the Angle Sum Theorem
Use theorems, conjectures, definitions and properties to indicate WHY? Each step can be used.

3. Theorem – Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180°.
mX + mY + mZ = 180° X Y Z

4. Example 1: Find the missing angle measures.
Find first because the measure of two angles of the triangle are known.
Angle Sum Theorem
Simplify.
Subtract 117 from each side.

5. Example 1: WHY??? Angle Sum Theorem Simplify.
Subtract 142 from each side.
Answer:

6. Your Turn:
Find the missing angle measures.
Answer:

7. Theorem – Third Angle Theorem
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent.
Abbreviation: If 2 s of one Δ are  to 2 s of another Δ, then third s are .

8. Example 2: Find the measure of each numbered angle in the figure.
WHY???
Exterior Angle Theorem
Simplify.
If 2 s form a linear pair, they are supplementary.
Substitution
Subtract 70 from each side.

9. Example 2 (continued): Exterior Angle Theorem Substitution
WHY???
Exterior Angle Theorem
Substitution
Subtract 64 from each side.
If 2 s form a linear pair, they are supplementary.
Substitution
Simplify.
Subtract 78 from each side.

10. Example 2 (continued) : Angle Sum Theorem Substitution Simplify.
WHY???
Angle Sum Theorem
Substitution
Simplify.
Subtract 143 from each side.
Answer:

11. Your Turn: Find the measure of each numbered angle in the figure.
Answer:

12. Corollaries
A corollary is a statement that can be easily proven using a theorem.
Corollary – The acute s of a right ∆ are complementary.
Corollary – There can be at most one right or obtuse  in a ∆.
Also called a Conjecture in our textbook.

13. Example 3:
GARDENING The flower bed shown is in the shape of a right triangle. Find if is 20.
WHY???
Corollary – At most 1 rt triangle
Substitution
Subtract 20 from each side.
Answer:

14. Your Turn:
The piece of quilt fabric is in the shape of a right triangle. Find if is 62.
Answer: