Page 77 - Math Course 3 (Book 2)

Angle Sum and Exterior Angle Theorems

∠1 and ∠2 are congruent vertical angles.
COROLLARIES So m∠2 = 63

9.1 The acute angles of a right angle are m∠3 + 63 + 79 = 180 Angle Sum Theorem.
complementary.
G
m∠3 + 142 = 180 Simplify.
Example: m∠G + m∠J = 90

J m∠3 = 38 Subtract 142 from each
H side.

9.2 There can be at most one right or obtuse
angle angle in a triangle.
Answer Therefore, m∠1 = 63, m∠2 = 63,
K P and m∠3 = 38
acute

142°
M L Q R Right Angles
acute
Example

Let’s Begin GARDENING
The flower bed shown is in the shape of a right
triangle. Find m∠A if m∠C is 20.

Interior Angles B C

Example

Find the missing angle measures.
A
Find m∠1first because the measure of two angles
of the triangle are known.
m∠A + m∠C = 90 Corollary 9.1

43° 79° m∠A + 20 = 90 Substitution

1 2
m∠A = 70 Subtract 20 from each side.
74°
3

Answer m∠A = 70
m∠1 + 43 + 74 = 180 Angle Sum Theorem.

m∠1 + 117 = 180 Simplify.

Subtract 117 from each
m∠1 = 63
side.

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