Determine the value of angle x in the second diagram.

Solution:

• The triangle inscribed in the circle has angles 50 degrees and the angle marked with arcs.
• Let the angle marked with arcs be y. So, $$50 + y + \text{third angle} = 180$$.
• The angle x is formed by the tangent and the chord.
• The angle subtended by the chord at the circumference is equal to the angle between the tangent and the chord through the point of contact.
• The angle marked with arcs 'y' is subtended by the arc which also subtends an angle of 50 degrees at the circumference.
• Therefore, the angle subtended by this arc at the circumference is 50 degrees.
• Thus, $$y = 50$$ degrees.
• Now, consider the triangle. The sum of angles is 180 degrees. One angle is 50 degrees. The angle subtended by the chord which forms angle x at the circumference is y. So, $$y$$ is also an angle in the triangle.
• We have an inscribed triangle with one angle 50 degrees. The angle x is formed by the tangent and a chord. This angle is equal to the angle in the alternate segment.
• The angle x subtends an arc. The angle subtended by the same arc at the circumference is 50 degrees.
• Therefore, x = 50 degrees.

Ответ: 50°