Theory question 104
Circle Theorems(a) In the diagram, QOS is a diameter, ∠RQS = x° and ∠QST = (3x + 15)°. Find: (i) the value of x. (ii) ∠RSQ.
(b) If 2N4seven = 15Nnine, find the value of N.
Show the model answer
Model answer
(a)(i) ∠QRS = 90° (angle in a semicircle)
∠QST is an exterior angle of triangle QRS: 3x + 15 = 90 + x → x = 37.5°
(ii) ∠RSQ = 180° − (3 × 37.5 + 15)° = 52.5° (or 90° − 37.5°)
(b) 2 × 49 + 7N + 4 = 81 + 45 + N → 102 + 7N = 126 + N → N = 4
Explanation
Use the angle in a semicircle and the exterior angle of a triangle.