Question

If ( m_∠ ABC = 80^∘ ), what is ( m_∠ DBC )? Justify your reasoning.

a) Using the Angle Addition Postulate, ( 20 + m_∠ DBC = 80 ). So, ( m_∠ DBC = 60^∘ ) using the subtraction property of equality.
b) Using the Angle Addition Postulate, ( 20 + 80 = m_∠ DBC ). So, ( m_∠ DBC = 100^∘ ) using the addition property of equality.
c) Using the addition property of equality, ( 20 + 80 = 100 ), so ( m_∠ DBC = 100^∘ ).
d) Using the subtraction property of equality, ( 80 - 20 = 60 ), so ( m_∠ DBC= 60^∘ ).

Answer 1

The correct measure of ∠ DBC is 60°, calculated by applying the Angle Addition Postulate and the subtraction property of equality to subtract 20° from 80°.

Step-by-step explanation:

To solve for the measure of ∠ DBC, we must apply our understanding of angles and the Angle Addition Postulate, which states that if a point D lies in the interior of ∠ ABC, then m∠ ABD + m∠ DBC = m∠ ABC. Given that m∠ ABC = 80° and assuming that part (a) suggests there is an angle m∠ ABD = 20°, we apply the postulate by stating: 20° + m∠ DBC = 80°. Using the subtraction property of equality, we would subtract 20° from both sides of the equation to find m∠ DBC. Hence:

m∠ DBC = 80° - 20° = 60°.

The correct answer is that m∠ DBC = 60°, which is found using the subtraction property of equality as explained above. This process is a fundamental skill in geometry, especially in solving for unknown angles.