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

Step-by-step 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.

Answer 2

Answer: d. 120 degrees

Step-by-step 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

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