Question

two parallel lines are crossed by a transversal. if m∠6 = 123.5°, then m∠1 is 56.5°. 67.5°. 123.5°. 136.5°.

Explanation:

Step1: Identify angle - pair relationship

$\angle6$ and $\angle3$ are alternate - interior angles. Since the two lines are parallel, $m\angle6=m\angle3 = 123.5^{\circ}$.

Step2: Identify supplementary angles

$\angle1$ and $\angle3$ are supplementary angles (a linear pair). So $m\angle1 + m\angle3=180^{\circ}$.

Step3: Solve for $m\angle1$

$m\angle1=180^{\circ}-m\angle3$. Substitute $m\angle3 = 123.5^{\circ}$ into the equation: $m\angle1=180 - 123.5=56.5^{\circ}$.

Answer:

$56.5^{\circ}$