). If YU = YV, ST = 16, mQS = 34,

and mRT = 98°, find each measure.

QR=8

QU=76

Measure of arc ST=114°

Measure of arc QR=114°

Measure of arc XT=57°

Step-by-step explanation:

Given that,

YU=YV

ST=16

mQS=34

mRT=98

We will use pythagoras theorem,

QR=8

QU=76

QR=ST

Since they span the same arc, let the arc be x.

360 - QS - RT = QR + ST

Recall that QR=ST

360 - 34 - 98 = x + x

228 = 2x

Divide both side by 2

X= 228/2

X=114°

Therefore, the measure of the arc ST and the arc QR=114°

Measure of span of arc XT will be:

= 1/2× (arc ST)

= 1/2 × 114

= 57°

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!