Answer:
x = 30
Step-by-step explanation:
AB is a tangent to the circle so ∠ ABO = 90°
The sum of the 3 angles in a triangle = 180° , then
x + 2x + 90 = 180
3x + 90 = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Answer: x = 30
OA cuts the circle (O) at C
because ∠ABC is the angle created by tangent rays and chord
=> ∠ABC = 1/2.∠AOB = 1/2.2x = x
ΔOBC has OB = OC (are both radii)
=> ΔOBC is the isosceles triangle at O
=> ∠OCB = (180° - ∠COB)/2 = (180° - 2x)/2 = 90° - x
because ∠OCB is the outer angle of ΔABC
=> ∠OCB = ∠ABC + ∠CAB
⇔ 90° - x = x + x
⇔ 90 = 3x
⇔ x = 30
Step-by-step explanation:
