Answer:
27.6°
Explanation:
You want the measure of base angle CDA in the trapezoid shown.
Pythagorean theorem
The side adjacent to angle CDA includes the length of base BC and the length of segment AE (refer to the attachment).
Segment AE is the short side of a 5-12-13 right triangle with scale factor 1/2. So, it is 2.5 cm. That means the length of segment DG in the attachment is ...
23 -2.5 -9 = 11.5 . . . . . . cm
Tangent
The tangent of angle CDA is ...
Tan = Opposite/Adjacent
tan(D) = (6 cm)/(11.5 cm)
D = arctan(6/11.5) ≈ 27.6°
The measure of angle D is 27.6°.
__
Additional comment
We have used our knowledge of Pythagorean triples to simplify the solution. If you need to compute length AE, you can use the Pythagorean theorem relation. It is ...
AE² +BE² = AB²
AE² = AB² -BE² = 6.5² -6² = 42.25 -36 = 6.25
AE = √6.25 = 2.5 . . . . . cm
Some Pythagorean triples commonly seen in school problems are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. A triangle with these side lengths is a right triangle. Any multiple or fraction of these side lengths will form a similar right triangle.
<95141404393>