a )
First of all we need to find the value of x ,
because the angles are written in terms of the variable x .
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Let's find the value of x :
STV angle & SUV angle have same measure because both of them are the front angle of SV arc .
[tex]STV angle \: = SUV angle \: \: = \frac{SV \: arc}{2} \\ [/tex]
So :
[tex]3x - 5 = 2x + 15[/tex]
Add sides 5
[tex]3x - 5 + 5 = 2x + 15 + 5[/tex]
[tex]3x = 2x + 20[/tex]
Subtract sides minus 2x
[tex]3x - 2x = 2x + 20 - 2x[/tex]
Collect like terms
[tex]x = 2x - 2x + 20[/tex]
[tex]x = 20[/tex]
Thus the measure of angle T equals :
[tex]measure \: of \: angle \: T = 3x - 5 \\ [/tex]
Now just need to put the value of x which we found :
[tex]measure \: of \: angle \: T \: = 3 \times (20) - 5 \\ [/tex]
[tex]measure \: of \: angle \: T \: = 60 - 5[/tex]
[tex]measure \: of \: angle \: T \: = 55°[/tex]
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b )
angle S & angle V are also have same measure because they both are the front angles to the TU arc .
And we need to find the value of x again in this part exactly like we did for a .
[tex]angle \: \: S = angle \: \: V[/tex]
As the question told :
[tex]angle \: \: S = 3x[/tex]
and ,
[tex]angle \: \: V = x + 16[/tex]
Thus :
[tex]3x = x + 16[/tex]
Subtract sides minus x
[tex]3x - x = x + 16 - x[/tex]
Collect like terms
[tex]2x = x - x + 16[/tex]
[tex]2x = 16[/tex]
Divide sides by 2
[tex] \frac{2x}{2} = \frac{16}{2} \\ [/tex]
Simplification
[tex]x = 8[/tex]
So ;
[tex]measure \: \: of \: \: angle \: \: S = 3x[/tex]
[tex]measure \: \: of \: \: angle \: \: S = 3(8)[/tex]
[tex]measure \: \: of \: \: angle \: \: S = 24°[/tex]
And we're done.
