An angle C of 72 ° is inscribed with a circle that touches the sides of the angle at points A

An angle C of 72 ° is inscribed with a circle that touches the sides of the angle at points A and B, where O is the center of the circle. Find the corner AOB.

Connecting point C with the center of the circle O, we get two triangles COB, and COA.
Since the circle is inscribed in the angle <ACB, the angles are <OAC = <OBC = 90 (degrees). The BCA angle is divided into two equal angles: <BCO = <ACO = 72/2 = 36 (degrees).
Now let’s find the required angle <AOB = <AOC + <BOC.
We define these angles from the triangles AOC and BOC: <AOC = 180 – 90 – <ACO = 54 (degrees). <BOC = 180 – 90 – <BCO = 90 – 36 = 54 (degrees).
<AOB = <AOC + <BOC = 54 + 54 = 108 (degrees).