Question

this triangle is equilateral. find the value of x. (6x + 6)° (9x - 21)° x = ?

Explanation:

Step1: Recall properties of equilateral triangles

In an equilateral triangle, all interior angles are equal, and each angle measures \(60^\circ\). So, the two given angles \((6x + 6)^\circ\) and \((9x - 21)^\circ\) should be equal to each other (and also equal to \(60^\circ\)). We can set up the equation:
\(6x + 6 = 9x - 21\)

Step2: Solve the equation for \(x\)

First, subtract \(6x\) from both sides:
\(6 = 3x - 21\)
Then, add \(21\) to both sides:
\(27 = 3x\)
Finally, divide both sides by \(3\):
\(x = 9\)

We can verify by plugging \(x = 9\) back into the angle expressions. For \(6x + 6\): \(6(9)+6 = 54 + 6 = 60^\circ\). For \(9x - 21\): \(9(9)-21 = 81 - 21 = 60^\circ\), which confirms the angles are equal (and \(60^\circ\) as expected for an equilateral triangle).

Answer:

\(x = 9\)