x = 30°.
The triangle drawn inside the circle is an equilateral and equiangular triangle which means that its three sides and its internal angles (that measure 60°) are equal.
To find x°:
First, we can see from the image that the tangent line to circle with arrows is formed a right angle, the angle of one side of the equilateral triangle, and the angle formed with the other side of the equilateral triangle, this three angles has to form 180° respect to the tangent line:
90° + 60° + y° = 180°
y° = 180° + 150°
y° = 30°
Second, the line in the right side of the equilateral triangle form an angle of 180°, so:
60° + z° = 180°
z° = 180° - 60°
z° = 120°
Finally, the triangle formed by this lines its internal angles are x°, y°, and z° and its sum is 180°, then:
x° + y° + z° = 180°
x° + 30° + 120° = 180°
x° + 150° = 180°
x° = 180° - 150°
x° = 30°
