Find the measure of angle x in the figure.

Question

90 degrees58 degrees nbspx

A ray that rises from right to left, a vertical ray pointing upward, and a horizontal ray pointing right have a common endpoint forming two angles measuring 58 degrees and 90 degrees. A third angle formed by the horizontal and rising ray is labeled x.
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Part 1
The measure of angle x is
  
enter your response heredegrees.

Answer 1

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 \( x \):

1. First, add \( 90^\circ \) and \( 58^\circ \): \[ 90^\circ + 58^\circ = 148^\circ \]

2. Now, subtract this sum from \( 360^\circ \) to find \( x \): \[ x = 360^\circ - 148^\circ = 212^\circ \]

Thus, the measure of angle \( x \) is \( 212^\circ \).