Question

use the angle measures to complete the statement.
triangle abc with angle a = 43.8°, angle b = 102.9°, angle c = 33.3°
options:
a) m∠a < m∠b < m∠c
b) m∠b < m∠c < m∠a
c) m∠c < m∠a < m∠b
d) m∠b < m∠a < m∠c

Explanation:

Step1: Identify angle measures

From the triangle, \( m\angle A = 43.8^\circ \), \( m\angle B = 102.9^\circ \), \( m\angle C = 33.3^\circ \).

Step2: Compare angle measures

• \( m\angle B = 102.9^\circ \), \( m\angle A = 43.8^\circ \), \( m\angle C = 33.3^\circ \)
• So, \( m\angle B > m\angle A > m\angle C \) (or \( m\angle B > m\angle A \) and \( m\angle A > m\angle C \), leading to \( m\angle B > m\angle A > m\angle C \)). Looking at the options, option b is \( m\angle B > m\angle C > m\angle A \)? Wait, no, wait: Wait, \( m\angle B = 102.9 \), \( m\angle A = 43.8 \), \( m\angle C = 33.3 \). So order from largest to smallest: \( B > A > C \)? Wait, no, \( 102.9 > 43.8 > 33.3 \), so \( m\angle B > m\angle A > m\angle C \). But the options: Let's check the options again. The options are:

a. \( m\angle A > m\angle B > m\angle C \) – No, 43.8 < 102.9.

b. \( m\angle B > m\angle C > m\angle A \) – 102.9 > 33.3 > 43.8? No, 33.3 < 43.8. Wait, maybe I misread. Wait, \( m\angle C = 33.3 \), \( m\angle A = 43.8 \), so \( m\angle A > m\angle C \). So \( m\angle B (102.9) > m\angle A (43.8) > m\angle C (33.3) \). But the options: Let's re-express the options:

Wait, the options are:

a. \( m\angle A > m\angle B > m\angle C \) – False.

b. \( m\angle B > m\angle C > m\angle A \) – False, because \( m\angle A = 43.8 > m\angle C = 33.3 \).

c. \( m\angle C > m\angle A > m\angle B \) – False.

d. \( m\angle B > m\angle A > m\angle C \) – Yes! Wait, 102.9 > 43.8 > 33.3, so \( m\angle B > m\angle A > m\angle C \), which is option d? Wait, no, the original options: Let me check the image again. The options are:

a. \( m\angle A > m\angle B > m\angle C \)

b. \( m\angle B > m\angle C > m\angle A \)

c. \( m\angle C > m\angle A > m\angle B \)

d. \( m\angle B > m\angle A > m\angle C \)

Ah, yes! So \( m\angle B = 102.9^\circ \), \( m\angle A = 43.8^\circ \), \( m\angle C = 33.3^\circ \). So \( 102.9 > 43.8 > 33.3 \), so \( m\angle B > m\angle A > m\angle C \), which is option d? Wait, no, wait the option d is \( m\angle B > m\angle A > m\angle C \)? Wait, the user's options: Let me recheck. The options are:

a. \( m\angle A > m\angle B > m\angle C \)

b. \( m\angle B > m\angle C > m\angle A \)

c. \( m\angle C > m\angle A > m\angle B \)

d. \( m\angle B > m\angle A > m\angle C \)

Yes, so \( m\angle B (102.9) > m\angle A (43.8) > m\angle C (33.3) \), so option d is correct. Wait, but earlier I thought maybe b, but no, \( m\angle A = 43.8 > m\angle C = 33.3 \), so \( m\angle B > m\angle A > m\angle C \), which is option d.

Answer:

d. \( m\angle B > m\angle A > m\angle C \)