The corner shop's round cafe table has four chair positions marked \(E\), \(F\), \(G\) and \(H\), fixed evenly around its circular edge to form a cyclic qua...
Question 1 Report
The corner shop's round cafe table has four chair positions marked \(E\), \(F\), \(G\) and \(H\), fixed evenly around its circular edge to form a cyclic quadrilateral. Angle \(E = (3x + 10)^{\circ}\) and the opposite angle \(G = (x + 30)^{\circ}\).
- Write an equation in \(x\) and solve it. (3)
- Write down the size of angle \(E\). (1)
Answer Details
This question tests the cyclic quadrilateral theorem: opposite angles of a quadrilateral inscribed in a circle sum to \(180^{\circ}\).
(a) Angles \(E\) and \(G\) are opposite angles of the cyclic quadrilateral \(EFGH\), so they must sum to \(180^{\circ}\):\[(3x + 10) + (x + 30) = 180\]\[4x + 40 = 180\]\[4x = 140\]\[x = 35\][3]
(b) Substituting back:\[\angle E = 3(35) + 10 = 115^{\circ}\][1]
Always check the substituted value against the other angle as a quick verification: angle \(G = 35 + 30 = 65^{\circ}\), and \(115^{\circ} + 65^{\circ} = 180^{\circ}\), confirming the answer is consistent.
Download The App On Google Playstore
Everything you need to excel in your exams
