Angle relationships in circle-Isosceles triangles in a circle- example

Angle relationships in circle-Isosceles triangles- example
Isosceles triangles in a circle- example

Since the angle ∠AOB is a central angle, the sides OA and OB are radii of the circle and therefore the triangle ABO is an isosceles triangle.
In an isosceles triangle the angles opposite the two equal sides are equal, therefore ∠OAB=∠ABO.
The sum of angles in a triangle is equal to 180°, therefore ∠OAB+∠ABO+∠AOB=180°.
We are given that ∠AOB=100° and we know that ∠OAB=∠ABO, therefore 100°+∠OAB+∠ABO=180°.
Marking by x the equal angles ∠OAB and ∠ABO we get an equation that we can solve:
100+2x =180
2x=80
x=40
The value of the angle ∠OAB is 40 degrees.

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