If YU=YV, ST=16, mQS=34, and mRT=98, find each measure.

Answer: QR=8; QU=76

Measure of the arc ST=114°

Measure of the arc QR=114°

Measure of the 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°