Question

Find the measure of arc QS.

Answer 1

180-128= 52 because a circles measurement is always 180, if we know GTS is 128 we subtract

Answer 2

The measure of arc QS is also 128 degrees.

To find the measure of arc QS, we can use the fact that the sum of the angles in a circle formed by intersecting chords is equal to the sum of their intercepted arcs.

Given:

PQS = 128 degrees

Firstly, let's establish the relationship between the angles and arcs:

Angle PQS corresponds to arc PRS (same intercepted arc).

Angle RQS corresponds to arc QS.

The sum of angles PQS and RQS equals the sum of their intercepted arcs:

Angle PQS + Angle RQS = Arc PRS + Arc QS

We know Angle PQS = 128 degrees and Arc PRS = 128 degrees.

128 degrees (Angle PQS) + Angle RQS = 128 degrees (Arc PRS) + Arc QS

Now, solve for Angle RQS (or Arc QS):

Angle RQS = 128 degrees + Arc QS - 128 degrees

Angle RQS = Arc QS

Therefore, Angle RQS = Arc QS.

So, the measure of arc QS is also 128 degrees.