Question

X=

a) 27
b) 54
c) 61

Answer 1

The measure of ∠x=27°

Answer 2

The measure of ∠x=27°

Explanation:

Given the figure

we have to find the value of x

As the arc AC is 68° i.e m arc(AC)=68°

By theorem, the angle subtended at the centre is twice the angle subtended at the circumference of circle i.e

m arc(AC)=2∠ABC

`\angle ABC=(1)/(2)m arc(AC)=(1)/(2)* 68=34^(\circ)`

As ∠BED=61°

∠AEB and ∠BED forms a linear pair therefore their sum adds up to 180°

∠AEB + ∠BED=180°

∠AEB =180°-61°=119°

In ΔAEB, by angle sum property

∠BAE+∠ABE+∠AEB=180°

x+34°+119°=180°

x=180°-34°-119°=27°

Hence, the measure of ∠x=27°

Option a is correct