To find the measure of angle \( x \), we can use the fact that the sum of the angles around a point is equal to \( 360^\circ \).
In the given configuration, you have three angles:
- One angle measuring \( 90^\circ \)
- Another angle measuring \( 58^\circ \)
- The angle we want to find, \( x \)
We can set up the equation based on the sum of the angles:
\[ 90^\circ + 58^\circ + x = 360^\circ \]
Now, we can solve for \( x \):
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First, add \( 90^\circ \) and \( 58^\circ \): \[ 90^\circ + 58^\circ = 148^\circ \]
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Now, subtract this sum from \( 360^\circ \) to find \( x \): \[ x = 360^\circ - 148^\circ = 212^\circ \]
Thus, the measure of angle \( x \) is \( 212^\circ \).