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In-s [12.5K]
3 years ago
6

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

Mathematics
2 answers:
posledela3 years ago
6 0

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.

madreJ [45]3 years ago
6 0

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}

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