(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°)