In the diagram, PR is a tangent to the circle at Q, QT//RS, < SQR = 35º and < RSQ = 50º. Find the value of <QST
- 40\(^o\)
- 65\(^o\)
- 85\(^o\)
-
95\(^o\)
The correct answer is: D
Explanation
In the diagram,
a = 50\(^o\) (alternate angles)
b\(_1\) + a + 35\(^o\) = 180\(^o\) (sum of angles on a straight line)
i.e; b\(_1\) + 50\(^o\) + 35\(^o\)
= 180º
b\(_1\) + 180\(^o\) - 85\(^o\) = 90\(^o\)
But b\(_2\) = \(b_1\) = 95\(^o\) (angles in alternate segment)