90.6k views
4 votes
If YU=YV,ST=16,mQS=34, and mRT=98, find each measure .

User Platypus
by
3.7k points

1 Answer

2 votes

Answer: QR=8 ; QU=76

Measure of the arc ST=114°

Measure of the arc QR=114°

Measure of the arc XT=57°

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°

User David Kean
by
5.3k points