Question

question 11: 71676
△abc is an equilateral triangle. m∠a = (3x - 12)°. solve for x.
a 14
b 19
c 20
d 24
e 34

Explanation:

Step1: Recall the property of an equilateral triangle

In an equilateral triangle, all angles are equal and each angle measures \(60^{\circ}\). So, \(m\angle A = 60^{\circ}\).

Step2: Set up the equation

Since \(m\angle A=(3x - 12)^{\circ}\) and \(m\angle A = 60^{\circ}\), we have the equation \(3x-12 = 60\).

Step3: Solve the equation for \(x\)

Add \(12\) to both sides of the equation: \(3x-12 + 12=60 + 12\), which simplifies to \(3x=72\).
Divide both sides by \(3\): \(x=\frac{72}{3}\).

Answer:

\(x = 24\), so the answer is D.