A minor arc is an arc that measures less than 180.
A major arc is an arc that measures greater than 180.
A semicircle is an arc with endpoints that lie on a diameter.
Type: Minor arc Measure: 127^(∘)
Practice makes perfect
An arc is a portion of a circle defined by two endpoints. A central angle separates the circle into two arcs — the major arc and the minor arc. The measures of these arcs are related to the measure of the central angle.
Arc
Measure
A minor arc is the shortest arc connecting two endpoints on a circle.
The measure is less than 180 and is equal to the measure of its related central angle.
A major arc is the longest arc connecting two endpoints on a circle.
The measure is greater than 180 and is equal to 360 minus the measure of the minor arc with the same endpoints.
The arc that we are looking at is ST. It is the shorter arc that connects the endpoints S and T. Therefore, ST is a minor arc.
To find its measure, we first need to find the measure of the major arc, SPT.
mSPT=mSR+mRQ+mQP+mPT
⇓
mSPT= 53+ 25+ 65+ 90=233
Now we will use that the measures of the major and the minor arc add to 360.
m ST+mSPT=360
⇓
m ST=360-mSPT=360-233=127
