Question

question 9 (1 point) (01.06 mc) what is m∠abc? justify your reasoning. a using the addition property of equality, 40 + 15 = 55, so m∠abc = 55°. b using the subtraction property of equality, 40 - 15 = 25, so m∠abc = 25°. c using the angle addition postulate, 15 + m∠abc = 40. so, m∠abc = 25° using the subtraction property of equality. d using the angle addition postulate, 15 + 40 = m∠abc. so, m∠abc = 55° after simplifying.

Explanation:

Step1: Recall Angle Addition Postulate

The Angle Addition Postulate states that if a point lies in the interior of an angle, the sum of the two smaller angles equals the larger angle. Here, ray BD is in the interior of ∠ABC, so \( m\angle ABC = m\angle ABD + m\angle DBC \).

Step2: Identify Angle Measures

From the diagram, \( m\angle ABD = 15^\circ \) and \( m\angle DBC = 40^\circ \).

Step3: Apply Postulate and Simplify

Using the Angle Addition Postulate, \( m\angle ABC = 15^\circ + 40^\circ \). Simplifying, \( 15 + 40 = 55 \), so \( m\angle ABC = 55^\circ \). Now check the options:

• Option a: Uses addition property but not the correct postulate reasoning.
• Option b: Incorrect subtraction, not matching the diagram.
• Option c: Incorrect equation (15 + m∠ABC = 40 is wrong).
• Option d: Correctly applies Angle Addition Postulate, sums 15 and 40 to get 55.

Answer:

d. Using the Angle Addition Postulate, \( 15 + 40 = m\angle ABC \). So, \( m\angle ABC = 55^\circ \) after simplifying.