A section of a roller coaster track forms a parallelogram ABCD.
If m∠ABC = 72°, what is m∠DAB?
Responses
A 72°72°
B 144°144°
C 216°216°
D 108°
A 72°
Since the opposite angles of a parallelogram are congruent, we know that m∠ABC = m∠CDA = 72°. Therefore, m∠BAD = 180° - m∠DAB - m∠DAB, since the angles of a triangle add up to 180°. Simplifying, we get m∠BAD = 180° - 2m∠DAB.
Since ABCD is a parallelogram, we know that m∠BAD = m∠ADC. Therefore, we can write:
m∠ADC = 180° - m∠CDA = 180° - 72° = 108°
Using the equation we found earlier, we can substitute in 108° for m∠BAD and solve for m∠DAB:
108° = 180° - 2m∠DAB
2m∠DAB = 72°
m∠DAB = 36°
Therefore, the answer is D) 108°.