Questions: Lines (L1) and (L2) are parallel lines. Determine the measures of (mathbfvarangle 1) through (mathbf4 12). [ mathrmm varangle 7=50^circ mathrmm varangle 1=50^circ mathrmm varangle 2=square^circ ]

Lines (L1) and (L2) are parallel lines. Determine the measures of (mathbfvarangle 1) through (mathbf4 12).
[
mathrmm varangle 7=50^circ
mathrmm varangle 1=50^circ
mathrmm varangle 2=square^circ
]

Transcript text: Lines $L_{1}$ and $L_{2}$ are parallel lines. Determine the measures of $\mathbf{\varangle 1}$ through $\mathbf{4} 12$. \[ \begin{array}{l} \mathrm{m} \varangle 7=50^{\circ} \\ \mathrm{m} \varangle 1=50^{\circ} \\ \mathrm{m} \varangle 2=\square^{\circ} \end{array} \]

Solution

Solution Steps

Step 1: Find m∠2

Angles ∠1 and ∠2 are supplementary angles, meaning they add up to 180°. Since m∠1 = 50°, m∠2 = 180° - 50° = 130°.

Step 2: Find m∠3

Angles ∠1, ∠2 and ∠3 form a straight line, which equals 180°. We know that m∠1 = 50° and from the previous step, we found that m∠2 = 130°, so ∠3 = 180° - 50° - 130° = 0°. Since ∠3 is shown in the diagram as a non-zero angle, angles 1 and 2 must actually add up to 180° and not include angle 3. Instead, angle 3 is supplementary with angle 2, meaning that m∠3 = 180° - 130° = 50°.

Step 3: Find m∠4

Angles ∠1 and ∠4 are vertical angles so they have an equal measure. Since m∠1 = 50°, m∠4 = 50°.