Question

1. line a is parallel to line b and m∠7 = 135. find m∠4. 45 135 145 35

Explanation:

Step1: Identify vertical - angle relationship

$\angle7$ and $\angle5$ are vertical angles, so $m\angle5 = m\angle7=135^{\circ}$ since vertical angles are equal.

Step2: Use corresponding - angle relationship

Since line $a$ is parallel to line $b$, $\angle5$ and $\angle1$ are corresponding angles. So $m\angle1 = m\angle5 = 135^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle1$ and $\angle4$ are supplementary angles (a linear - pair), so $m\angle1+m\angle4 = 180^{\circ}$.

Step4: Solve for $m\angle4$

$m\angle4=180^{\circ}-m\angle1$. Substitute $m\angle1 = 135^{\circ}$ into the equation: $m\angle4 = 180 - 135=45^{\circ}$.

Answer:

$45$