Determine the value of angle x in the second figure.

Solution:

• The figure shows an inscribed angle of 50° in a circle.
• The angle at the center subtended by the same arc as the inscribed angle is twice the inscribed angle. Therefore, the central angle is 2 * 50° = 100°.
• The angle marked as x is formed by a tangent and a chord. The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
• The angle in the alternate segment subtended by the chord is 50°.
• Therefore, x = 50°.

Answer: 50°