Question

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

Answer 1

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.