Question

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

Answer 1

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 .

$STV angle \: = SUV angle \: \: = \frac{SV \: arc}{2}$

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 :

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

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

$measure \: of \: angle \: T \: = 55°$

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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

$\frac{2x}{2} = \frac{16}{2}$

Simplification

$x = 8$

So ;

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

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

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

And we're done.