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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.

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 class=

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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,

[tex]tanD=\frac{AE}{DE}[/tex]

         [tex]=\frac{3}{2}[/tex]

D = [tex]tan^{-1}(1.5)[/tex]

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.

Ver imagen eudora

a. The measure of angle ∠D = 56°.

b) The measure of AD = √13.

Calculation of the measure of the angle:

Since ABCD is a trapezoid with parallel sides AB and CD.

Now We have to determine the measure of ∠D from the given figure

[tex]tan D = AE \div DE\\\\ = 3\div 2\\\\D = tan^{-1}(1.5)\\\\[/tex]

= 56 degrees

b. Now the measure of AD should be

AD² = AE² + DE²

      = 3² + 2²

AD² = 9 + 4

AD = √13

Hence, Length of AD is √13 in.

learn more about length here: https://brainly.com/question/1571309

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