Question

1. 9x + 8° 4x + 18° type of angle pair: choose your answer... these angles are: choose your answer... equation: choose your answer... x = type your answer... measure of the 9x + 8 angle = type your answer... measure of the 4x + 18 angle = type your answer...

Explanation:

Step1: Identify angle - pair type

Assume the two lines are parallel and the angles are alternate - interior angles (a common scenario). Alternate - interior angles are equal.

Step2: Set up the equation

Since the two angles $9x + 8$ and $4x+18$ are equal (if they are alternate - interior angles), we set up the equation $9x + 8=4x + 18$.

Step3: Solve the equation for x

Subtract $4x$ from both sides: $9x-4x + 8=4x-4x + 18$, which simplifies to $5x+8 = 18$. Then subtract 8 from both sides: $5x+8 - 8=18 - 8$, so $5x=10$. Divide both sides by 5: $x=\frac{10}{5}=2$.

Step4: Find the measure of the first angle

Substitute $x = 2$ into $9x + 8$. We get $9\times2+8=18 + 8=26$.

Step5: Find the measure of the second angle

Substitute $x = 2$ into $4x + 18$. We get $4\times2+18=8 + 18=26$.

Answer:

Type of angle pair: Alternate - interior angles
These angles are: Equal
Equation: $9x + 8=4x + 18$
$x = 2$
Measure of the $9x + 8$ angle $=26$
Measure of the $4x + 18$ angle $=26$