Question

Find the value of x ​

Answer 1

Answer:

110°

Step-by-step explanation:

In triangle AOB

OA = OB (radii of same circle)

$m\angle OAB = m\angle OBA =20\degree$

$m\angle AOB = 180\degree - (20\degree +20\degree)$

$m\angle AOB = 180\degree - 40\degree$

$m\angle AOB = 140\degree$

$m\widehat {ACB} =m\angle AOB = 140\degree$

(measure of minor arc is equal to corresponding central angle)

$x\degree = \frac{1}{2} (360\degree - 140\degree)$

(inscribed angle theorem)

$x\degree = \frac{1}{2} \times 220\degree$

$\huge\purple {x = 110}$