Respuesta :

calculista

we know that

The minor arc ST is equal to the angle ∠SOT by central angle

∠SOT=∠ROU ------> by vertical angles

In this problem we have

∠ROU=[tex]94\°[/tex]

substitute

∠SOT=[tex]94\°[/tex]

so

minor arc ST=[tex]94\°[/tex]

Find the major arc SRT

we know that

The major arc plus the minor arc is equal to [tex]360\°[/tex]

minor arc ST+major arc RST=[tex]360\°[/tex]

Solve for major arc RST

major arc RST=[tex]360\°-94\°=266\°[/tex]

therefore

the answer is

[tex]266\°[/tex]

The major arc ST  in the given figure is 266 degree.

Given-

In the given figure RT and SU are the diameters of the circle O. The value of angle ROU is 94 degree.

Here in given figure the value of angle ROU and SOT are the verticle angles.Vertical angles are a pair of opposite angles formed by intersecting lines where the value of both the angle is equal.Therefore,

[tex]\angle ROU =\angle SOT =94^{\circ}[/tex]

Now minor arc ST is equal to the angle SOT by the central angle (central Angle is the angle formed by two arms with the center of a circle as the vertex). Therefore minor arc ST is 94 degree.

Relation between minor arc and major arc can be formulated as,

[tex]Major \ arc + Minor \ arc = 360[/tex]

[tex]Major \ arc \ ST + Minor \ arc \ ST = 360[/tex]

[tex]Major \ arc \ ST+94 = 360[/tex]

[tex]Major \ arc \ ST = 360-94[/tex]

[tex]Major \ arc \ ST =266^{\circ}[/tex]

Hence, the major arc ST is 266 degree.

For more about the circle, follow the link below-

https://brainly.com/question/11833983

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