Question

In the figure below, lines that appear to be tangent are tangent. Point O is the center of the circle. Which of the following is the value of x?

a. 60 degrees
b. 90 degrees
c. 100 degrees
d. 120 degrees

Answer 1

Answer: d. 120 degrees

Explanation:

From the given figure drawn, we can see that

∠ABC=60°

Also we know that tangents are radius are perpendicular at the point of tangency

And ∠OAB=∠OCB=90° (∵ tangents are radius are perpendicular at the point of tangency)

Therefore, we have

`\angle{AOC}+\angle{OCB}+\angle{ABC}+\angle{OAB}=360^(\circ)\text{ ( By Angle sum property of quadrilateral)}\\\\\Rightrarrow\ x+90^(\circ)+60^(\circ)+90^(\circ)=360^(\circ)\\\\\Rightarrow\ x=360^(\circ)-240^(\circ)\\\\\Rightarrow\ x=120^(\circ)`

Answer 2

(D) 120 degrees

Explanation:

From the figure drawn, we have

∠ABC=60°

And ∠OAB=∠OCB=90° (angles made by tangent on the circle is 90°)

Thus, ∠AOC+∠OCB∠CBA+∠OAB=360° (Angles sum property of quadrilateral)

`x+90^(\circ)+90^(\circ)+60^(\circ)=360^(\circ)`

`x+240^(\circ)=360^(\circ)`

`x=120^(\circ)`

Therefore, the value of x is
`120^(\circ)`

Hence, option D is correct.