To solve your problem, we need to analyze the relationship between the angles given that \( m\angle 2 = 137^\circ \).
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Finding \( m\angle 1 \): Since angles 1 and 2 are on a straight line, they are supplementary angles. Thus, we can use the following equation: \[ m\angle 1 + m\angle 2 = 180^\circ \] Substituting \( m\angle 2 = 137^\circ \): \[ m\angle 1 + 137^\circ = 180^\circ \] \[ m\angle 1 = 180^\circ - 137^\circ = 43^\circ \]
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Finding \( m\angle 3 \): Angles 2 and 3 are vertical angles, meaning they are equal: \[ m\angle 3 = m\angle 2 = 137^\circ \]
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Finding \( m\angle 4 \): Angles 1 and 4 are also vertical angles, implying they are equal: \[ m\angle 4 = m\angle 1 = 43^\circ \]
To summarize the calculations:
- \( m\angle 1 = 43^\circ \)
- \( m\angle 3 = 137^\circ \)
- \( m\angle 4 = 43^\circ \)
So the final answers are:
- \( m\angle 1 = 43^\circ \)
- \( m\angle 3 = 137^\circ \)
- \( m\angle 4 = 43^\circ \)