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maw [93]
3 years ago
10

What is the length of the shorter base of the Little Trapezoid trail?

Mathematics
1 answer:
valentina_108 [34]3 years ago
3 0

Answer:

The length of the shorter base of the little trapezoid trail is 1 mi.

Step-by-step explanation:

Let the shorter base of the large trapezoid is S and the larger base of the large trapezoid is L.

Similarly, assume that the shorter base of the small trapezoid is s and the larger base of the small trapezoid is l.

Since, the trapezoids are similar, so

\frac{L}{l} = \frac{S}{s}

Now, given that S = 2 mi, L = 8 mi and l = 4 mi and we have to find s.

So, s = \frac{S \times l}{L} = \frac{4 \times 2}{8} = 1 mi. (Answer)

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Answer:

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Step-by-step explanation:

∠ESK is the supplement of ∠EDK, so is 100°. ∠ESD = 1/2·arc ED, so is 25°. Since ...

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_____

Regarding opposite angles of an inscribed quadrilateral

Chord EK divides the 360° circle into two arc: major arc EDK and minor arc ESK. The sum of those arcs is 360°. Each of the inscribed angles that intercepts those arcs has half the measure of the arc. That is, ∠ESK intercepts arc EDK, so has half its measure. Likewise, ∠EDK intercepts arc ESK, so has half its measure. The sum of those opposite angles will be the sum of half the measures of the arcs, so half the sum of the arcs, or 1/2·360° = 180°.

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