Question

1. given (mangle4 = 3x) and (mangle5=6x). find the value of (x) for which line (a) is parallel to line (b).

Explanation:

Step1: Recall parallel - line property

When two lines are parallel, corresponding angles are equal. $\angle4$ and $\angle5$ are alternate - interior angles. For lines $a$ and $b$ to be parallel, $\angle4=\angle5$ (alternate - interior angles are equal when lines are parallel).

Step2: Set up the equation

Given $m\angle4 = 3x$ and $m\angle5=6x - 30$, we set up the equation $3x=6x - 30$.

Step3: Solve the equation for $x$

Subtract $3x$ from both sides: $0 = 6x-3x - 30$.
This simplifies to $0 = 3x - 30$.
Add 30 to both sides: $30 = 3x$.
Divide both sides by 3: $x = 10$.

Answer:

10