Page 134 - Math Course 2 (Book 2)

Triangle Properties of Inequalities

By the Exterior Angle Inequality Theorem, Exterior Angles
m∠14 > m∠4, m∠14 > m∠11, m∠14 > m∠2,
and m∠14 > m∠4 + m∠3.

Since ∠11 and ∠9 are vertical angles, they have
equal measure, so m∠14 > m∠9. m∠9 > m∠6 and
m∠9 > m∠7, so m∠14 > m∠6 and m∠14 > m∠7.

Thus, the measures of ∠4,
Answer ∠11, ∠9, ∠3, ∠2, ∠6, and ∠7
are all greater than m∠14. Use the Exterior Angle Inequality Theorem to list all
angles whose measures are less than m∠8.

Use the Exterior Angle Inequality Theorem to list all A. ∠2, ∠5, ∠7
angles whose measures are less than m∠5. B. ∠2, ∠5, ∠8, ∠7
14 C. ∠1, ∠2, ∠5, ∠6, ∠7, ∠8
17 D. ∠2, ∠3, ∠5, ∠6, ∠7, ∠8
16 3 4 5 6 15
10 11 12 Answer
2 9
1 8 7

By the Exterior Angle Inequality Theorem,
m∠10 > m∠5, m∠16 > m∠10 so m∠16 > m∠5,
and m∠17 > m∠5 + m∠6, m∠15 > m∠12, and
m∠12 > m∠5, so m∠15 > m∠5.

Thus, the measures of ∠10,
Answer ∠16, ∠12, ∠15, and ∠17 are
all greater than m∠5.

Use the Exterior Angle Inequality Theorem to list all
Your Turn! angles whose measures are less than m∠4.

A. ∠4, ∠5
Compare Angle Measures B. ∠4, ∠4, ∠5
C. ∠4, ∠5, ∠9
Determine which angle has the greatest measure. D. ∠1, ∠4, ∠5, ∠9

Answer

A. ∠1
B. ∠3
C. ∠5
D. ∠4

Answer

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