Question

I was wondering if someone can check my work. It has to do with circles, tangent etc.

Pic below....

Answer 1

I got B.

I used Theorem 12-13 for solving \(\Large{x}\). The formula is….


\(\Huge{m \angle 1= \frac{1}{2}(x+y)}\)

In which I substituted 60 for x and 70 for y…..

\(\Huge{m \angle 1= \frac{130}{2}}\)

In which I got the total of 65 degrees….I then subtract that number by 180 to find x in which I got 115 degrees for x…..

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For \(\Large{y}\) I used Theorem 12-14 which is….

\(\Huge{m \angle 1= \frac{1}{2}(x-y)}\)

In which I substituted 180 as \(\Large{x}\) since it is the opposite angle and I substituted the total with 53…..

\(\LARGE{53=\frac{180-y}{2} \rightarrow 106=180-y \rightarrow 180-106=74=y}\)
I got the total of 74 degrees for \(\Large{y}\) so the answer I got was B.

Am I correct?

Answer 2

ok I did get 115 degrees for x...

and yes we know 60/2+70/2+x=180
since the sum of the angles of a triangle are 180 deg