Identify the properties of AOC.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the properties of $\triangle AOC$.
$OA$ and $OC$ are radii of the circle. Therefore, $OA = OC$.
This means $\triangle AOC$ is an isosceles triangle.
Step 2: Determine the base angles of $\triangle AOC$.
In an isosceles triangle, the angles opposite the equal sides are equal.
Given $\angle OAC = 20^\circ$.
Since $OA = OC$, then $\angle OCA = \angle OAC$.
$$\angle OCA = 20^\circ$$
Step 3: Calculate $x$ using the sum of angles in a triangle.
The sum of angles in any triangle is $180^\circ$.
In $\triangle AOC$:
$$\angle AOC + \angle OAC + \angle OCA = 180^\circ$$
Substitute the known values:
$$x + 20^\circ + 20^\circ = 180^\circ$$
$$x + 40^\circ = 180^\circ$$
$$x = 180^\circ - 40^\circ$$
$$x = 140^\circ$$
$$\boxed{x = 140^\circ}$$
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