2010 WAEC Mathematics Theory (a)&nbsp; In the diagram, &lt; PQR = 125&deg;, &lt; QRS = r, &lt; RST =...

(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.

(a) \(\therefore r = 36° + 55° = 91°\)

(b)

\(< BAS = 60°\) (angles in alternate segments)

\(< BAE = 180° - 5x°\) (adjacent angles on a transversal)

\(\therefore < BAS + < BAE + < EAT = 180°\)

\(\therefore 60° + 180° - 5x + x = 180°\)

\(\implies 240° - 180° = 4x\)

\(60° = 4x \implies x = \frac{60}{4} = 15°\)

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