Adjacent angles ABD and DBC. The measure of angle ABD is 15 degrees, and the measure of angle DBC is 40 degrees.
What is m∠ABC? Justify your reasoning.
Using the addition property of equality, 40 + 15 = 55, so m∠ABC = 55°.
Using the subtraction property of equality, 40 − 15 = 25, so m∠ABC = 25°.
Using the Angle Addition Postulate, 15 + m∠ABC = 40. So m∠ABC = 25° using the subtraction property of equality.
Using the Angle Addition Postulate, 15 + 40 = m∠ABC. So m∠ABC = 55° after simplifying.
None of the reasoning provided justifies why m∠ABC is either 55° or 25°.
To find the measure of angle ABC, we can use the fact that the sum of the measures of adjacent angles is equal to the measure of the larger angle formed by the two adjacent angles. In this case, angle ABC is the larger angle formed by angles ABD and DBC.
So, we have:
m∠ABD + m∠DBC = m∠ABC
Substituting in the given measurements, we have:
15° + 40° = m∠ABC
Simplifying, we find:
55° = m∠ABC
Therefore, the measure of angle ABC is 55°.