By the Congruent Supplements Theorem, we can conclude that,
∠FBC ≅ ∠DBG.
What is Congruent Supplements Theorem?
The Congruent Supplements Theorem states that two angles are said to be congruent if they are supplements of the same angle or even congruent angles.
If there are 4 lines such that, right angles are created when a horizontal line with the points F, B, and G crosses a vertical line with the points A, B, and E at point B. Between angles F and B and A and G, a third diagonal line with the points D, B, and C is intersecting the other two lines at point B. At points A, C, and G, there is a fourth line that joins three other lines.
Drawing Conclusion
In case the angle FBC and angle CBG are supplementary angles, angle DBG and angle DBF are another pair of supplementary angles, and angle CBG is-congruent-to angle DBF, we can apply congruent supplement theorem and draw the following inference,
∠FBC ≅ ∠DBG
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