Math / Geometry

Question8)

Studdy Solution

STEP 1

1. Vertical angles are congruent (equal in measure).
2. We are solving for $x$ .

STEP 2

1. Set up an equation using the property of vertical angles.
2. Solve for $x$ .

STEP 3

Recognize that vertical angles are equal. Therefore, we can set the expressions for the angles equal to each other:
$2.5x + 5 = 26x$

STEP 4

To solve for $x$ , first isolate $x$ on one side of the equation. Start by subtracting $2.5x$ from both sides:
$2.5x + 5 - 2.5x = 26x - 2.5x$ $5 = 23.5x$

STEP 5

Now, divide both sides by $23.5$ to solve for $x$ :
$x = \frac{5}{23.5}$

STEP 6

Calculate the value of $x$ by performing the division:
$x \approx 0.2128$
The value of $x$ is approximately:
$\boxed{0.2128}$

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