Question

day 3 - review for unit 3 test
if ∠1 and ∠2 are alternate interior angles and ∠1 = 70°, find ∠2.
given ∠a = 2x + 10 and ∠b = 80, and ∠a and ∠b are corresponding angles, solve for x.
fill in the blank: if two lines are perpendicular, their slopes are ______.

Explanation:

Step1: Recall alternate - interior angles property

When two parallel lines are cut by a transversal, alternate - interior angles are equal. Since $\angle1$ and $\angle2$ are alternate - interior angles and $\angle1 = 70^{\circ}$, then $\angle2=\angle1$.
$\angle2 = 70^{\circ}$

Step2: Recall corresponding angles property

When two parallel lines are cut by a transversal, corresponding angles are equal. Given $\angle A=2x + 10$ and $\angle B = 80$, and $\angle A$ and $\angle B$ are corresponding angles, we set up the equation $2x+10 = 80$.
$2x+10=80$

Step3: Solve the equation for x

Subtract 10 from both sides of the equation: $2x=80 - 10$.
$2x=70$
Then divide both sides by 2: $x=\frac{70}{2}$.
$x = 35$

Step4: Recall slope property of perpendicular lines

If two lines are perpendicular, their slopes are negative reciprocals of each other.

Answer:

$\angle2 = 70^{\circ}$
$x = 35$
negative reciprocals of each other