Question

this triangle is equilateral. find the value of x. (10x - 20)° (8x - 4)° x = ?

Explanation:

Step1: Recall equilateral triangle angles

In an equilateral triangle, all angles are equal (each \(60^\circ\)), and also, since it's equilateral, all angles are equal, so we can set the two given angle expressions equal.
\(10x - 20 = 8x - 4\)

Step2: Solve for x

Subtract \(8x\) from both sides:
\(10x - 8x - 20 = 8x - 8x - 4\)
\(2x - 20 = -4\)
Add 20 to both sides:
\(2x - 20 + 20 = -4 + 20\)
\(2x = 16\)
Divide both sides by 2:
\(x=\frac{16}{2}=8\)
We can also verify by checking the angle: \(10(8)-20 = 60\), \(8(8)-4 = 60\), which matches the equilateral triangle angle.

Answer:

\(x = 8\)