>Find m∠BAC and m∠DAB in the figure shown below.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." width="169" height="70" align="middle" style="border: 0px solid; vertical-align: middle;"
∠s EAD and BAC are vertical angles, so they are congruent.
The ∠s DAB and EAB are supplementary to them, and are also congruent.
Not sure why you typed all that garbage above, rather than just naming the angles and lines. and infusing HTML style info.
To find m∠BAC and m∠DAB, we need to analyze the given figure.
From the figure, we know that line DC intersects with line EB at point A. The angle EAD is labeled as 80 degrees.
To find m∠BAC, we need to look for a relationship between angle EAD and angle BAC. We can use the fact that when a line intersects two parallel lines, the alternate interior angles are congruent.
Since line DC intersects line EB, we can determine that line DC is parallel to line EB. Therefore, angle EAD and angle BAC are alternate interior angles, and they are congruent. Therefore, m∠BAC is also 80 degrees.
To find m∠DAB, we can use the fact that the angles on a straight line add up to 180 degrees. Since angle EAD is 80 degrees, angle DAB must be the supplement of angle EAD.
To find the supplement of an angle, we subtract the given angle from 180 degrees. So, m∠DAB = 180 degrees - 80 degrees = 100 degrees.
Therefore, m∠BAC is 80 degrees and m∠DAB is 100 degrees.