Final Answer:
C) 6x + 3 an equilateral triangle has three congruent sides and three 60-degree angles. Solving the equation for the angles in triangle ABC results in x = 60 degrees. Upon matching this value with the expression provided in the answer choices, only option C) 6x + 3 fits, with x = 10, resulting in 63 as the final value.
Step-by-step explanation:
In an equilateral triangle, all three sides are congruent, and all three angles measure 60 degrees. Each angle in an equilateral triangle measures 60 degrees. The sum of the angles in a triangle is always 180 degrees. Therefore, the equation representing the sum of the angles in triangle ABC is 60 + 60 + x = 180, where x represents the third angle. By solving for x, we get x = 60 degrees.
Now, we know that the three angles in triangle ABC are all 60 degrees. To find the value of x if AABC is equilateral, we need to consider the expression given for x in the answer choices. Among the options, only option C) 6x + 3 matches the value we found for x, which is 60 degrees, when x = 10. So, the value of x if AABC is equilateral is 6x + 3, where x = 10, resulting in 6(10) + 3 = 63.
In summary, an equilateral triangle has three congruent sides and three 60-degree angles. Solving the equation for the angles in triangle ABC results in x = 60 degrees. Upon matching this value with the expression provided in the answer choices, only option C) 6x + 3 fits, with x = 10, resulting in 63 as the final value.