If O is the center of the circle, find the value of x in the following figure (using the given information) :

Label the points as shown in the figure below:

Arc AD subtends ∠AOD = 70° at center.

⇒ ∠AOD = 2∠ABD (∵ angle subtended by an arc at the center = double the angle subtended by it any point on the remaining part of the circle.)

⇒ 70° = 2∠ABD
⇒ ∠ABD = $\dfrac{70°}{2}$
⇒ ∠ABD = 35°

∠ABM = ∠ABD.

Considering △ABM,

Since sum of angles in a triangle is equal to 180°.

⇒ ∠AMB + ∠ABM + ∠BAM = 180°.
⇒ 90° + 35° + x° = 180°
⇒ x° + 125° = 180°
⇒ x° = 55°.

Hence, the value of x = 55.