Theory question 103
Angles and Polygons(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.
Show the model answer
Model answer
(a) PQ ∥ UT. Draw lines through R and S parallel to them.
QR makes 180° − 125° = 55° with the parallel through R.
ST makes 44° with the parallel through S (alternate to ∠STU), so RS makes 80° − 44° = 36° with it, and also 36° at R.
r = 55° + 36° = 91°.
(b) ∠ACB = ∠ADB = 60° (same segment), so ∠SAB = 60° (alternate segment).
On the straight line SAT: ∠BAE = 180° − 60° − x.
AB ∥ CE, so ∠BAE + ∠AEC = 180° (co-interior): 120° − x + 5x = 180°, so x = 15°.
Explanation
Draw extra parallel lines through each corner of a zig-zag.