Angle AOC in the given figure

Given that AOB is a straight line, and we need to find the angle AOC in the figure.

Understanding the figure

- The given figure has a triangle AOC with A, O and C as its vertices.
- AOB is a straight line which intersects the triangle at O.
- Angle AOB is given as 90 degrees.

Using angle sum property

- We know that the sum of angles in a triangle is 180 degrees.
- Let us consider the triangle AOC. We can write the following equation:
- angle AOC + angle OCA + angle OAC = 180 degrees
- We know that angle OCA and angle OAC are equal as they are opposite angles. Let's assume their value as x.
- Hence, we can write the equation as:
- angle AOC + 2x = 180 degrees

Using angle OCB

- Let us consider the triangle OCB. We know that the sum of angles in a triangle is 180 degrees.
- We can write the following equation for the triangle OCB:
- angle OCB + angle OBC + angle BOC = 180 degrees
- We know that angle OCB and angle OBC are equal as they are opposite angles. Let's assume their value as y.
- We also know that angle BOC is 90 degrees as given in the figure.
- Hence, we can write the equation as:
- y + y + 90 degrees = 180 degrees
- 2y = 90 degrees
- y = 45 degrees

Calculating angle AOC

- We can substitute the value of y in the equation we got earlier:
- angle AOC + 2(45 degrees) = 180 degrees
- angle AOC + 90 degrees = 180 degrees
- angle AOC = 90 degrees

Final answer

- Hence, the value of angle AOC is 90 degrees in the given figure.