Question

1. a rainbow forms when sunlight reflects off raindrops at different angles. for blue light, the measure of ∠2 is (14x - 1)° and the measure of ∠1 is (12x + 17)°. what is the angle relationship shown? how would you set up the equation? x = measure of angle 1 = degrees

Explanation:

Step1: Identify angle - relationship

Assume the angles are vertical angles (since no other information about their position is given and vertical angles are equal).

Step2: Set up the equation

Set the two angle - measures equal to each other: $14x - 1=12x + 17$.

Step3: Solve the equation for x

Subtract $12x$ from both sides: $14x-12x - 1=12x-12x + 17$, which simplifies to $2x-1 = 17$. Then add 1 to both sides: $2x-1 + 1=17 + 1$, so $2x=18$. Divide both sides by 2: $x=\frac{18}{2}=9$.

Step4: Find the measure of angle 1

Substitute $x = 9$ into the expression for angle 1: $12x+17=12\times9 + 17=108 + 17=125$.

Answer:

What is the angle relationship shown? Vertical angles
How would you set up the equation? $14x - 1=12x + 17$
$x = 9$
measure of angle 1 = 125 degrees