Given that angles <1 and <3 are vertical angles, they are equal in measure. Since you stated that their measures are both equal to 68 degrees, we can use that information to find the value of \( x \).
From the options provided, let’s analyze the equations:
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2x + 68 = 180: This equation suggests that there is another angle (possibly <2 or <4) which is supplementary to either <1 or <3, and would be equal to \( 180 - 68 = 112 \). This equation can be used to solve for \( x \) in this context, but actually isn’t necessary for angles <1 and <3 if they are already known to equal 68.
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68x = 2: This doesn’t appear to relate to the measure of angles and does not make sense in this context.
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x = 68: This implies that the variable \( x \) takes on the value 68 directly, which doesn’t apply to the angles without knowing how \( x \) is defined in relation to them.
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2x = 68: This could be interpreted as another equation used to define either angle properly, leading to \( x = 34 \).
The correct way to set up these equations would actually focus purely on the angles of interest.
Since <1 and <3 measure 68 degrees, there is actually no need to solve for any additional variable related to the angle's measures. Thus, the relevant equation for <1 or <3 simply affirms: \[ <1 = <3 = 68^\circ \]
If you want to solve for \( x \) (without any further context tying \( x \) to <1 and <3), and if you assumed another angle was determined as supplementary, then \( 2x + 68 = 180 \) might be used to figure out another angle’s measure when set to 180 degrees:
Rearranging \( 2x + 68 = 180 \): \[ 2x = 180 - 68 \] \[ 2x = 112 \] \[ x = 56 \]
However, based on your initial message, simply accepting that <1 and <3 are both equal to 68 degrees suffices for solving the angle situation without introducing unnecessary variables.
To summarize:
- The correct measures of angles <1 and <3 are both 68 degrees.
- To relate \( x \) to angles <1 and <3 in any way in the equations provided would require further context.