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

User Imsky
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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=(1)/(2)(m(arc(SW))-m(arc(TV)))


6x-19=(1)/(2)((12x-5)-(2x+7))


6x-19=(1)/(2)(12x-5-2x-7)


6x-19=(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.

If mSW = (12x-5)°, mTV= (2x+7)°,and m angle TUV = (6x-19)°, find mSW-example-1
User Artelius
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