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Liula [17]
3 years ago
8

If mSW = (12x-5)°, mTV= (2x+7)°,and m angle TUV = (6x-19)°, find mSW

Mathematics
1 answer:
svet-max [94.6K]3 years ago
7 0

Given:

Consider the below figure attached with this question.

m(arc(SW)) = (12x-5)°, m(arc(TV))= (2x+7)°,and measure of angle TUV = (6x-19)°.

To find:

The m(arc SW).

Solution:

Intersecting secant theorem: If two secants intersect outside the circle, then the angle on the intersection is half of the difference of the larger subtended arc and smaller subtended arc.

Using Intersecting secant theorem, we get

m\angle TUV=\dfrac{1}{2}(m(arc(SW))-m(arc(TV)))

6x-19=\dfrac{1}{2}((12x-5)-(2x+7))

6x-19=\dfrac{1}{2}(12x-5-2x-7)

6x-19=\dfrac{1}{2}(10x-12)

Multiply both sides by 2.

2(6x-19)=10x-12

12x-38=10x-12

12x-10x=38-12

2x=26

Divide both sides by 2.

x=13

Now, the measure of arc SW is:

m(arc(SW))=(12x-5)^\circ

m(arc(SW))=(12(13)-5)^\circ

m(arc(SW))=(156-5)^\circ

m(arc(SW))=151^\circ

Therefore, the measure of arc SW is 151 degrees.

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If you draw a picture with 2 cliffs and a river in the middle, you have find 2 right triangles. In each triangle the adjacent side to our known angle is the river of 90 feet. And the unknown side is the opposite leg.

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