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Verizon [17]
2 years ago
14

One base of an isosceles trapezoid is 12 and the other is 20. What is the length of the midsegment?

Mathematics
1 answer:
mr_godi [17]2 years ago
6 0
The length of the midsegment of an isosceles trapezoid is the sum of the two bases, divided by 2. So this means -

(base 1+base2) / 2

(12+20) / 2

32/2

Length of midsegment = 16
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Can someone help me and explain what to do here?
Vesna [10]

Answer:

 ∠STU = 69°

Step-by-step explanation:

The angle with vertex T is called an "inscribed angle." It intercepts arc SU. The relationship you are asked to remember is that the measure of the inscribed angle (T) is half the measure of the arc SU.

Point V is taken to be the center of the circle. The angle with vertex V is called a "central angle." It also intercepts arc SU. The relationship you are asked to remember is that the measure of the central angle (V) is equal to the measure of arc SU.

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Using these two relationships together, we realize angle V is twice the measure of angle T:

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  18x +12° = 2(18x -57°) . . . . . . relationship between the marked angles

  18x +12° = 36x -114° . . . . . eliminate parentheses

  126° = 18x . . . . . . . . . . . add 114°-18x

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_____

<em>Additional comment</em>

You may notice we did not solve for x. We only needed to know the value of 18x, so we stopped when we found that value. (Actually, we only need the value of 18x-57°. See below.)

__

<em>Alternate solution</em>:

  (18x +12°) -(18x -57°) = 18x -57° . . . . . . . subtract 18x -57° from both sides of the first equation.

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