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Questions (a,b), 1 (a,b)

Questions (a,b), 1 (a,b)-example-1
User ChenSmile
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a )

First of all we need to find the value of x ,

because the angles are written in terms of the variable x .

______________________________________

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 .


STV angle \: = SUV angle \: \: = (SV \: arc)/(2) \\

So :


3x - 5 = 2x + 15

Add sides 5


3x - 5 + 5 = 2x + 15 + 5


3x = 2x + 20

Subtract sides minus 2x


3x - 2x = 2x + 20 - 2x

Collect like terms


x = 2x - 2x + 20


x = 20

Thus the measure of angle T equals :


measure \: of \: angle \: T = 3x - 5 \\

Now just need to put the value of x which we found :


measure \: of \: angle \: T \: = 3 * (20) - 5 \\


measure \: of \: angle \: T \: = 60 - 5


measure \: of \: angle \: T \: = 55°

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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 .


angle \: \: S = angle \: \: V

As the question told :


angle \: \: S = 3x

and ,


angle \: \: V = x + 16

Thus :


3x = x + 16

Subtract sides minus x


3x - x = x + 16 - x

Collect like terms


2x = x - x + 16


2x = 16

Divide sides by 2


(2x)/(2) = (16)/(2) \\

Simplification


x = 8

So ;


measure \: \: of \: \: angle \: \: S = 3x


measure \: \: of \: \: angle \: \: S = 3(8)


measure \: \: of \: \: angle \: \: S = 24°

And we're done.

User Seandavi
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