Question

Mark (✓) against the correct answer in each of the following:
In the given figure, ABDC and ABFE are cyclic quadrilaterals. If ∠ACD = 110°, then ∠AEF = ?
(a) 55°
(b) 70°
(c) 90°
(d) 110°

Answer 1

(d) 110°

Since ACDE is a cylic quadrilateral, so

$$\begin{gathered} \angle B+\angle C=180° \\ \Rightarrow \angle B=180°-\angle C=180°-110°=70° \end{gathered}$$
Again, AEFB is a cylic quadrilateral.
So,
$$\begin{gathered} \angle B+\angle E=180° \\ \Rightarrow \angle E=180°-\angle B=180°-70°=110° \end{gathered}$$
$\mathrm{i}.\mathrm{e}.\angle AEF=110°$