F5 Maths

In the figure: ABCD is a circle. If arc AB : arc BC: arc CD : arc DA = 1 : 2: 3 : 3 and E is a point lying on BD, then angle CAE =

The answer is: B. 50°


∠BAC
= 180° x [(arc BC)/(arc AB + arc BC + arc CD + arc CA)]
= 180° x [2/(1 + 2 + 3 + 3)]
= 40°

∠ABE
= = 180° x [(arc DA)/(arc AB + arc BC + arc CD + arc CA)]
= 180° x [3/(1 + 2 + 3 + 3)]
= 60°

In ΔABE, sum of interior angles:
∠ABE + ∠BAE + ∠AEB = 180°
∠ABE + (∠BAC + ∠CAE) + ∠AEB = 180°
60° + (40° + ∠CAE) + 30° = 180°
∠CAE = 50°

arc AC: arc BC: arc CD : arc DA = 1:2:3:3

or

arc AB: arc BC: arc CD : arc DA = 1:2:3:3 ?

or

any other typing error ?