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Examples to show how to use the property that the measure of a central angle is equal to the measure of its intercepted arc to find the missing measures of arcs and angles in given figures.
To find the angle of a triangle within a circle segment, you first need to determine the central angle of the circle segment. Then, you can use the properties of triangles inscribed in circles to find the angle. The angle of the triangle within the circle segment will be half the measure of the central angle.
Area of sector/Area of circle = Angle of sector/360o Area of sector = (Area of circle*Angle of sector)/360o
The 4 interior angles of a quadrilateral add up to 360 degrees. 360-65-90-60 = 145 degrees which is the missing angle