Math  /  Geometry

Questioni.

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx where two intersecting lines create equal angles. Watch out! Don't forget that angles formed by intersecting lines are equal, not supplementary!

STEP 2

1. Set up the equation
2. Solve for *x*

STEP 3

When two lines intersect, the angles opposite each other are called **vertical angles**, and they're **equal**!
So, we know that 2x+172x + 17 and 3x43x - 4 represent the same angle measure.

STEP 4

Let's write this relationship as an equation: 2x+17=3x42x + 17 = 3x - 4 This equation says that the measure of the first angle, 2x+172x + 17, is equal to the measure of the second angle, 3x43x - 4.

STEP 5

Let's get all the xx terms on one side.
We can subtract 2x2x from both sides of the equation: 2x+172x=3x42x2x + 17 - 2x = 3x - 4 - 2x 17=x417 = x - 4Now, all the *x* terms are nicely isolated on one side!

STEP 6

We want to get xx all by itself.
Let's add 4 to both sides of the equation to move the constant term to the other side: 17+4=x4+417 + 4 = x - 4 + 4 21=x21 = xBoom! We've found that x=21x = \mathbf{21}!

STEP 7

The value of xx is 21\mathbf{21}.

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