The key thing here was remembering that same side interior angles are supplementary and that base angles in an isosceles trapezoid are always congruent. So A we said was 110 and D we said was 70 degrees. Sum of the measures of the interior angles of a n-gon is (2)180. The sum of the angles of a triangle is 180. All polygons can be separated into triangles. Just in case, let us also recall that a trapezoid is a geometric shape with four sides such that at least one pair of sides is parallel to each other.If there are two such pairs, then we get a parallelogram. So I’m going to write that D must be 70 degrees and on that A must be 110 degrees. Notice that the pentagon is made into 3 triangles. An isosceles trapezoid is a trapezoid with legs that have the same length (compare to isosceles triangles). Hence, the measure of the other two angles of an isosceles triangle is 55°. Now you just have to remember that your base angles are congruent to each other. Let the measure of the unequal angle is 70° and the other two equal angles measures x then, as per the angle sum rule, 70° + x + x 180°. So I’m going to write in here that C must be 70 degrees. So if B is 110 C must be what? 180 minus 110 which 70 degrees. Well I know that these two must be supplementary because they are on the same side of this transversal BC. If I look at the only thing that we know about this trapezoid that’s angle B which is 110 degrees, I could start of by finding angle C. We also know that the same side interior angles here, so I’m looking at these triangles right here, are going to be supplementary that’s the definition of same side interior. Well we see that the base angles, so if I’m looking at two base angles, they are going to be congruent to each other. So let’s go over and take a look at what we know about isosceles trapezoids. In this problem we have an isosceles trapezoid which means we have two legs that are congruent when we have a pair of parallel sides.
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