Question

additional details were added for this assignment. statements reasons m || n given m∠1 = 120° ∠5 ≅ ∠1 m∠5 = m∠1 angle congruence postulate m∠5 = 120° substitution property of equality m∠6 + m∠5 = 180° m∠6 + 120° = 180° substitution property of equality m∠6 = 60° subtraction property of equality

Explanation:

Step1: Identify vertical - angles

$\angle5$ and $\angle1$ are vertical - angles. Vertical angles are congruent.

Step2: Apply angle - congruence postulate

Since $\angle5\cong\angle1$, by the Angle Congruence Postulate, $m\angle5 = m\angle1$.

Step3: Substitute the value of $m\angle1$

Given $m\angle1 = 120^{\circ}$, substituting into $m\angle5 = m\angle1$ gives $m\angle5=120^{\circ}$ by the Substitution Property of Equality.

Step4: Identify supplementary angles

$\angle6$ and $\angle5$ are supplementary angles (linear - pair), so $m\angle6 + m\angle5=180^{\circ}$.

Step5: Substitute the value of $m\angle5$

Substitute $m\angle5 = 120^{\circ}$ into $m\angle6 + m\angle5 = 180^{\circ}$, getting $m\angle6+120^{\circ}=180^{\circ}$ by the Substitution Property of Equality.

Step6: Solve for $m\angle6$

Using the Subtraction Property of Equality, subtract $120^{\circ}$ from both sides of $m\angle6 + 120^{\circ}=180^{\circ}$. So $m\angle6=180^{\circ}-120^{\circ}=60^{\circ}$.

Answer:

$m\angle6 = 60^{\circ}$