Question

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

Explanation:

Step1: Recall equilateral triangle angles

In an equilateral triangle, all angles are equal and each angle measures \(60^\circ\).

Step2: Set up equation for angles

Since the triangle is equilateral, the two given angles \((6x + 6)^\circ\) and \((9x - 21)^\circ\) are equal (and also equal to \(60^\circ\)). So we set \(6x + 6 = 9x - 21\) (or we could set either equal to \(60\), but solving \(6x + 6 = 9x - 21\) is simpler here).

Step3: Solve for \(x\)

Subtract \(6x\) from both sides: \(6 = 3x - 21\).
Add \(21\) to both sides: \(27 = 3x\).
Divide both sides by \(3\): \(x = 9\).
(We can verify: \(6(9)+6 = 60\), \(9(9)-21 = 60\), which matches the equilateral triangle angle measure.)

Answer:

9