Question

this triangle is isosceles.
find the value of x.

\\(x = ?\\)

Explanation:

Identify the properties of the given triangle

The problem states that the triangle is isosceles. The tick marks on the two sides indicate that those two sides are congruent (equal in length). According to the Base Angles Theorem, the angles opposite the congruent sides of an isosceles triangle are also congruent (equal in measure).

Set up the equation

Since the base angles are congruent, we can set their measures equal to each other:

$$ 8x + 2 = 6x + 14 $$

Solve for x

Subtract \(6x\) from both sides of the equation:

$$ 2x + 2 = 14 $$

Subtract 2 from both sides:

$$ 2x = 12 $$

Divide by 2:

$$ x = 6 $$

Answer:

This triangle is isosceles. Find the value of x.

\(x =\) <blank>6</blank>