If measurement of arc ST = 71 degrees, calculate m<SXT?
picture:
http://i121.photobucket.com/albums/o...oryz/002-8.jpg
answers:
a.) 54.5 degrees
b.) 71 degrees
c.) 109 degrees
d.) 142 degrees
If measurement of arc ST = 71 degrees, calculate m<SXT?
picture:
http://i121.photobucket.com/albums/o...oryz/002-8.jpg
answers:
a.) 54.5 degrees
b.) 71 degrees
c.) 109 degrees
d.) 142 degrees
Hello MuneebYou need two facts here:
- The angle between a tangent to a circle and the radius at the point of contact is $\displaystyle 90^o$.
- The angles of a quadrilateral add up to $\displaystyle 360^o$.
So $\displaystyle \angle XSR = \angle XTR =90^o$.
You are given that the arc ST subtends an angle of $\displaystyle 71^o$ at the centre of the circle. So $\displaystyle \angle SRT = 71^o$.
So $\displaystyle \angle SXT = 360 - (90+90+71) = 109^o$
Grandad