Answer:
Step-by-step explanation:
we know that
The area of the figure is equal to the area of rectangle (figure 1) plus the area of trapezoid (figure 2)
see the attached figure to better understand the problem
The area of the rectangle is
The area of the trapezoid is
The area of the figure is
From the given information, we get the value of ABC = 120°.
<h3>How to estimate the value of ABC?</h3>
Given: In the figure, O exists the center of the circle and OABC exists as a parallelogram.
Now, the radius of the circle exists
OA = OB = OC
Opposite sides of a parallelogram are equal
AB = OC and OA = BC
In ∆OAB,
OA = OB = AB and,
In ∆OCB,
OC = OB = BC
Therefore, ∆OAB and ∆OCB exist in equilateral triangles.
All angles of an equilateral triangle are equivalent to 60°.
Hence, ∠ABC = ∠OBA + ∠OBC
∠ABC = 60° + 60°
∠ABC = 120°
Therefore, the value of ∠ABC = 120°.
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