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.
1 answer:
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,
D =
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.
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Answer: A) 126.6
<u>Step-by-step explanation:</u>
Since we know ∠B = 85° and ∠C = 53°, we can use the Triangle Sum Theorem (angles of a triangle = 180°) to calculate ∠A.
∠A + ∠B + ∠C = 180
∠A + 85 + 53 = 180
∠A + 138 = 180
∠A = 42
Now we have:
A = 42 B = 85 C = 53
a = 85 b = ??? c = ???
We have all of the information for ∠A and side a so we can use the Law of Sines to find b (AC).