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Sedaia [141]
3 years ago
10

In circle o,SU is a diameter What is MST

Mathematics
2 answers:
Rom4ik [11]3 years ago
7 0

We have been given that SU is diameter of our circle so measure of arc ST will be equal measure of central angle SOT.

Diameter is longest line segment of a circle passing through center of circle. So angles formed by our diameter (straight line) will add up-to 180 degrees.

Let us set sum of measures of our angles equal to 180. We have been given that angle SOR and UOT are congruent angles, so we will set our equation as:

2(9x+5)+13x+15=180

Upon distributing 2 we will get,

18x+10+13x+15=180

31x+25=180

31x=180-25

31x=155

x=\frac{155}{31} =5

We can find measure of angle SOT by sum of measures of angle ROT and UOT.

\angle SOT=(13x+15)+(9x+5)

\angle SOT=13x+15+9x+5

Let us combine like terms.

\angle SOT=22x+20

Let us substitute x=5 in our given equation.

\angle SOT=22\cdot 5+20

\angle SOT=110+20=130

Therefore, measure of arc ST will be 130 degrees.

erik [133]3 years ago
6 0
It's 130 hope the answer helps
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