Question

Finding x - cicrle theorems

Answer 1

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

Explanation:

Answer 2

x = 30

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