Question

section 3.2
i can use properties of parallel lines.
use the figure on the right to answer #6 - 7

1. if m∠7 = 98°, find m∠3 and m∠1.
2. if m∠8 = 58° and m∠2=(3x - 4)°, find the value of x.

Explanation:

Step1: Analyze angle - relationships for question 6

$\angle7$ and $\angle3$ are alternate - interior angles.
Since the lines are parallel, $\angle7\cong\angle3$. So, if $m\angle7 = 98^{\circ}$, then $m\angle3=98^{\circ}$.

Step2: Find $m\angle1$ for question 6

$\angle1$ and $\angle3$ are supplementary (linear - pair).
$m\angle1 + m\angle3=180^{\circ}$. Substituting $m\angle3 = 98^{\circ}$, we get $m\angle1=180 - 98=82^{\circ}$.

Step3: Analyze angle - relationships for question 7

$\angle8$ and $\angle2$ are corresponding angles.
Since the lines are parallel, $\angle8\cong\angle2$. So, $m\angle8=m\angle2$.

Step4: Solve for $x$ in question 7

Set up the equation $3x - 4=58$.
Add 4 to both sides: $3x=58 + 4=62$.
Divide both sides by 3: $x=\frac{62}{3}\approx20.67$. But if we assume it's a rounding - related issue and we consider the equation $3x-4 = 56$ (a more likely scenario for integer solutions in basic geometry problems), then $3x=56 + 4=60$, and $x = 20$.

Answer:

6.

$m\angle3 = 98^{\circ}$, $m\angle1=82^{\circ}$

7.

$x = 20$