(a) 
In the diagram, < PQR = 125°, < QRS = r, < RST = 80° and < STU = 44°. Calculate the value of r.
(b) 
In the diagram TS is a tangent to the circle at A. AB // CE, < AEC = 5x°, < ADB = 60° and < TAE = x. Find the value of x.
Explanation
(a) 
\(\therefore r = 36° + 55° = 91°\)
(b) 
\(< BAS = 60°\) (angles in alternate segments)
\(< BAE = 180° - 5x°\) (adjacent angles on a transversal)
\(\therefore < BAS + < BAE + < EAT = 180°\)
\(\therefore 60° + 180° - 5x + x = 180°\)
\(\implies 240° - 180° = 4x\)
\(60° = 4x \implies x = \frac{60}{4} = 15°\)