Math Help - Geometry Help

1. Geometry Help

If measurement of arc ST = 71 degrees, calculate m<SXT?

picture:

http://i121.photobucket.com/albums/o...oryz/002-8.jpg

a.) 54.5 degrees
b.) 71 degrees
c.) 109 degrees
d.) 142 degrees

2. Are you allowed to use the fact that the internal angles of a quadrilateral add up to 360 degrees?

If so, note that RSXT is a quadrilateral whose angles you know all of except for the one you are being asked to find.

3. Originally Posted by Muneeb
If measurement of arc ST = 71 degrees, calculate m<SXT?
...
m < SXT

The picture does not identify "m"
I do not know what "m" is or how you could possibly
detemine whether it is greater, equal or less that "sxt"

Could you elaborate?

4. Hello Muneeb
Originally Posted by Muneeb
If measurement of arc ST = 71 degrees, calculate m<SXT?

picture:

http://i121.photobucket.com/albums/o...oryz/002-8.jpg

a.) 54.5 degrees
b.) 71 degrees
c.) 109 degrees
d.) 142 degrees
You need two facts here:

• The angle between a tangent to a circle and the radius at the point of contact is $90^o$.

• The angles of a quadrilateral add up to $360^o$.

So $\angle XSR = \angle XTR =90^o$.

You are given that the arc ST subtends an angle of $71^o$ at the centre of the circle. So $\angle SRT = 71^o$.

So $\angle SXT = 360 - (90+90+71) = 109^o$

5. Originally Posted by aidan
m < SXT

The picture does not identify "m"
I do not know what "m" is or how you could possibly
detemine whether it is greater, equal or less that "sxt"

Could you elaborate?
In this context "m < SXT" means "the measure of the angle SXT".

I'd normally write it $\angle SXT$ but I appreciate different notation is used in various places.