The problem asks to find the value of $x$ given that a circle is divided into three angles: $189^\circ$, $148^\circ$, and $x^\circ$.

GeometryAnglesCirclesEquation Solving
2025/4/28

1. Problem Description

The problem asks to find the value of xx given that a circle is divided into three angles: 189189^\circ, 148148^\circ, and xx^\circ.

2. Solution Steps

The sum of the angles in a full circle is 360360^\circ. Therefore, the sum of the three given angles must be equal to 360360^\circ.
189+148+x=360189^\circ + 148^\circ + x^\circ = 360^\circ
First, we add 189189 and 148148:
189+148=337189 + 148 = 337
So, we have:
337+x=360337 + x = 360
Now, we subtract 337337 from both sides of the equation to solve for xx:
x=360337x = 360 - 337
x=23x = 23

3. Final Answer

The value of xx is 23.

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