X = 27 54 61 i need help, someone please explain

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

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

Step-by-step explanation:

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)