Question

Adjacent angles abd and dbc. the measure of angle abd is 20 degrees. if m∠abc = 80°, what is m∠dbc? justify your reasoning. using the angle addition postulate, 20 m∠dbc = 80. so m∠dbc = 60° using the subtraction property of equality. using the angle addition postulate, 20 80 = m∠dbc. so m∠dbc = 100° using the addition property of equality. using the addition property of equality, 20 80 = 100, so m∠dbc = 100°. using the subtraction property of equality, 80 − 20 = 60, so m∠dbc = 60°.

Answer 1

The measure of angle DBC is 60°.

Step-by-step explanation:

Using the angle addition postulate, we know that the sum of adjacent angles is equal to the measure of the larger angle. Since m∠ABC is 80° and m∠ABD is 20°, we can use the angle addition postulate to set up the equation: 20 + m∠DBC = 80.

Simplifying the equation, we have: m∠DBC = 80 - 20 = 60°. Therefore, the measure of angle DBC is 60°.

Justification: The angle addition postulate allows us to set up the equation 20 + m∠DBC = 80. We can then solve for m∠DBC by subtracting 20 from both sides of the equation. This gives us m∠DBC = 60°.

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