Question

6. trapezoid ABCD shown below, AB|| DC, overline BC perp overline DC and sides have lengths as shown (aDetermine the measure of angle D to the nearest degree.

Answer 1

Answer:

a). ∠D = 56°

b). AD = √13

Step-by-step explanation:

(a) From the figure attached, ABCD is a trapezoid with parallel sides AB and CD. We have to find the measure of ∠D from the given figure.

From triangle ADE,

$tanD=\frac{AE}{DE}$

         $=\frac{3}{2}$

D = $tan^{-1}(1.5)$

D = 56.31

D ≈ 56°

Therefore, measure of ∠D is 56°.

(b). Now by applying Pythagoras theorem in ΔADE,

AD² = AE² + DE²

       = 3² + 2²

AD² = 9 + 4

AD = √13

Length of AD is √13 in.