Question

this triangle is equilateral.
find the value of (x).

(x = ?)

((6x + 12)^circ)

((8x - 4)^circ)

Explanation:

Identify properties of an equilateral triangle

Using the Isosceles Triangle Theorem and Base Angles Theorem knowledge points

$$ \text{An equilateral triangle is equiangular, meaning all its interior angles are equal.} $$

$$ \text{Each interior angle of an equilateral triangle measures } 60^\circ. $$

Set up equations for the given angles

Using the Isosceles Triangle Theorem and Base Angles Theorem knowledge points

$$ 6x + 12 = 60 $$

$$ 8x - 4 = 60 $$

Solve for x using the first angle equation

Using the Isosceles Triangle Theorem and Base Angles Theorem knowledge points

$$
LATEXBLOCK0
$$

Verify the solution with the second angle equation

Using the Isosceles Triangle Theorem and Base Angles Theorem knowledge points

$$
LATEXBLOCK1
$$

Answer:

This triangle is equilateral. Find the value of x.

\(x =\) <blank>8</blank>