Question 1(Multiple Choice Worth 1 points)

Question

(01.06 MC)

Adjacent angles ABD and DBC. The measure of angle DBC is 40 degrees.

If m∠ABC = 70°, what is m∠ABD? Justify your reasoning.

Using the addition property of equality, 40 + 70 = 110, so m∠ABD = 110°.
Using the subtraction property of equality, 70 − 30 = 40, so m∠ABD = 30°.
Using the Angle Addition Postulate, 40 + m∠ABD = 70. So m∠ABD = 30° using the subtraction property of equality.
Using the Angle Addition Postulate, 40 + 70 = m∠ABD. So m∠ABD = 110° using the addition property of equality.

Answer 1

To solve for m∠ABD given that the measure of angle DBC is 40 degrees and m∠ABC is 70 degrees, we can use the Angle Addition Postulate.

According to the Angle Addition Postulate, if we have two adjacent angles, their measures can be added together to find the measure of the larger angle formed. In this case, we have:

m∠ABC = m∠ABD + m∠DBC

Plugging in the values we know:

70 = m∠ABD + 40

Now, we can solve for m∠ABD:

m∠ABD = 70 - 40 m∠ABD = 30°

Thus, the correct justification is:

Using the Angle Addition Postulate, 40 + m∠ABD = 70. So m∠ABD = 30° using the subtraction property of equality.