Which reason justifies the statement that measure angle upper D upper A upper B is 100°?
Line upper D upper C is shown intersecting with line upper E upper B at point upper A. The angle upper E upper A upper D is labeled 80 degrees.
(1 point)
Responses
Angle D A Band angle Upper E Upper A Upper Dare supplementary.
Image with alt text: Angle D A B and Image with alt text: angle Upper E Upper A Upper D are supplementary.
Angle D A Band angle Upper E Upper A Upper Dare complementary.
Image with alt text: Angle D A B and Image with alt text: angle Upper E Upper A Upper D are complementary.
angle Upper D Upper A Upper B congruent-to angle Upper E Upper A Upper D
Image with alt text: angle Upper D Upper A Upper B congruent-to angle Upper E Upper A Upper D
angle Upper D Upper A Upper B perpendicular-to angle Upper E Upper A Upper D
None of the reasons listed justify the statement that measure angle DAB is 100°.
The reason that justifies the statement that angle DAB is 100° is that angle DAB is congruent to angle EAD.
To determine the reason that justifies the statement that angle DAB is 100°, we need to analyze the given information.
Given:
- Line DC intersects with line EB at point A.
- The angle EAD is labeled as 80 degrees.
To find the measure of angle DAB, we need to consider the relationship between the angles formed when a line intersects two other lines. In this case, the lines DC and EB intersect at point A, forming multiple angles.
Since angle DAB and angle EAD share a common ray (DA), and they are on opposite sides of the transversal DC, it suggests that they are supplementary angles.
Supplementary angles are two angles that add up to 180 degrees. Therefore, if angle EAD is 80 degrees, and it is supplementary to angle DAB, we can subtract 80 from 180 to find the measure of angle DAB:
180 - 80 = 100 degrees.
Hence, the justified reason for stating that angle DAB is 100° is that angle DAB and angle EAD are supplementary.