(a)
In the diagram, < PQR = 125^\circ, < QRS = r, < RST = 80^\circ and < STU = 44^\circ. Calculate the value of r.
(b) In the diagram TS is a tangent to the circle at A. AB // CE, < AEC = 5x^\circ, < ADB = 60^\circ and < TAE = x. Find the value of x.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) \(\therefore r = 36^\circ + 55^\circ = 91^\circ\)
(b)
\(< BAS = 60^\circ\) (angles in alternate segments)
\(< BAE = 180^\circ - 5x^\circ\) (adjacent angles on a transversal)
\(\therefore < BAS + < BAE + < EAT = 180^\circ\)
\(\therefore 60^\circ + 180^\circ - 5x + x = 180^\circ\)
\(\implies 240^\circ - 180^\circ = 4x\)
\(60^\circ = 4x \implies x = \frac{60}{4} = 15^\circ\)
Source: Myschool Past Questions Archive (Record #52803)