x=a) 27b) 54c) 61

Accepted Solution

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.em 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