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# ​ PLS HELP ME

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Somebody help me

Mar 1, 2021

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To be honest, I do not recall the correct way to do this problem. Of course, that assumes that there is a "correct" way, but I will just show you my method, and I hope that it makes sense to you! I also created a diagram. Admittedly, this was probably not necessary, but I did it anyway.

OC = OA = OB because those lengths represent radii of the circle O, and the radius of a circle is constant.

Therefore, $$\triangle OCA$$ is isosceles, and so is $$\triangle OBA$$. Because they are isosceles triangles, the angles opposite those congruent sides have the same measure.

Therefore, $$m\angle OCA = m\angle OCB = 18^\circ$$

By angle addition, $$m\angle ACB = 36^\circ$$.

Now, figure $$ACBO$$ is a quadrilateral, so that means that the sum of the interior angles is 360. We already know 3 of the angles, so let's find the 4th and final angle.

$$\text{4th interior angle } = 360 - (18 + 18 + 36)\\ \text{4th interior angle } = 360 - 72\\ \text{4th interior angle } = 288$$

$$m\angle AOB = 360 - \text{4th interior angle}\\ m\angle AOB = 360 - 288\\ m\angle AOB = 72^\circ$$

I hoped this helped you on your solving adventures!

Mar 1, 2021