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 degreesb. 90 degreesc. 100 degreesd. 120 degrees

Accepted Solution

Answer:(D) 120 degreesStep-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.