Math / Geometry

QuestionQ Solve for $x$ .
11 6 50 16

Studdy Solution

STEP 1

1. The problem involves a triangle with three angles.
2. The angles of a triangle sum up to $180^\circ$ .
3. We are given the angles $70^\circ$ , $60^\circ$ , and $8x + 2$ .
4. We need to solve for $x$ .

STEP 2

1. Set up the equation based on the sum of angles in a triangle.
2. Solve the equation for $x$ .

STEP 3

Use the fact that the sum of the angles in a triangle is $180^\circ$ . Set up the equation:
$70^\circ + 60^\circ + (8x + 2) = 180^\circ$

STEP 4

Simplify the equation by combining like terms:
$130^\circ + 8x + 2 = 180^\circ$

STEP 5

Further simplify the equation:
$132^\circ + 8x = 180^\circ$

STEP 6

Isolate the term with $x$ by subtracting $132^\circ$ from both sides:
$8x = 180^\circ - 132^\circ$

STEP 7

Calculate the right side of the equation:
$8x = 48^\circ$

STEP 8

Solve for $x$ by dividing both sides by 8:
$x = \frac{48^\circ}{8}$

STEP 9

Calculate the value of $x$ :
$x = 6$
The solution for $x$ is:
$\boxed{6}$

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