ABCD is an isosceles trapezoid. Angle CDA = 80. Find the measure of angle BAD.
Two of the angles in this trapezoid are 80 and two are 100. I do not have your figure so do not know which.
To find the measure of angle BAD in an isosceles trapezoid ABCD, we need to use the properties of isosceles trapezoids.
An isosceles trapezoid has two opposite angles that are congruent. In this case, angle CDA is given as 80 degrees. Since angle CDA is congruent to angle CBA (as they are opposite angles in an isosceles trapezoid), we can conclude that angle CBA is also 80 degrees.
Now, let's look at the angles within triangle ABD. The sum of the angles in a triangle is always 180 degrees. In triangle ABD, angles BAD, ABD, and BDA add up to 180 degrees. We have found that angle ABD (which is the same as angle CBA) is 80 degrees.
So, we can set up the equation: BAD + ABD + BDA = 180 degrees. Plugging in the values we know, we get: BAD + 80 degrees + BDA = 180 degrees.
Since BDA and BAD are adjacent angles and they share the side BD, they must add up to 180 degrees. Therefore, BDA = 180 degrees - BAD.
Substituting this into our equation, we get: BAD + 80 degrees + (180 degrees - BAD) = 180 degrees.
Simplifying, we have: BAD + 80 degrees + 180 degrees - BAD = 180 degrees.
By combining like terms, we get: 260 degrees = 180 degrees.
However, this is not possible since 260 degrees is greater than 180 degrees.
Therefore, there is no solution for the measure of angle BAD given the given information.