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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

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 d class=

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boffeemadrid

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)

[tex]x+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}[/tex]

[tex]x+240^{\circ}=360^{\circ}[/tex]

[tex]x=120^{\circ}[/tex]

Therefore, the value of x is [tex]120^{\circ}[/tex]

Hence, option D is correct.

Ver imagen boffeemadrid
JeanaShupp

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

[tex]\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} [/tex]