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3 years ago

Can someone help me and explain what to do here?

Mathematics

1 answer:

Vesna [10]3 years ago

4 0

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.

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

∠SVU = 2×∠STU

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

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

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

∠STU = 18x -57° = 126° -57°

∠STU = 69°

_____

Additional comment

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.)

Alternate solution:

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

69° = 18x -57° . . . . . simplify. This is the answer to the problem.

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