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Identify the properties of AOC.

April 20, 2026Mathematics

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Answer

x = 140^\circ

3 steps

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.
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 $\angle OCA = \angle OAC$ .
$\angle OCA = 20^\circ$
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:
$x + 20^\circ + 20^\circ = 180^\circ$ $x + 40^\circ = 180^\circ$ $x = 180^\circ - 40^\circ$ $x = 140^\circ$

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