Answer:
The measure of ∠x=27°
Step-by-step 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
[tex]\angle ABC=\frac{1}{2}m arc(AC)=\frac{1}{2}\times 68=34^{\circ}[/tex]
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
