Answer:
x = 3
Step-by-step explanation:
Given an equilateral triangle whose two sides have measures of m∠(5x + 3)° and m∠(7x - 3)°.
We can establish the following equality statement since both sides have the same measure:
5x + 3 = 7x - 3
To start with, add 3 to both sides of the equation:
5x + 3 + 3 = 7x - 3 + 3
5x + 6 = 7x
Next, subtract 5x from both sides:
5x -5x + 6 = 7x - 5x
6 = 2x
Divide both sides by 2 to solve for x:
[tex]\mathsf{\frac{6}{2} = \frac{2x}{2}}[/tex]
x = 3
Therefore, the value of x = 3.
Substitute the value of x into the equality statement to find the measures of the sides of the given triangle:
5x + 3 = 7x - 3
5(3) + 3 = 7(3) - 3
15 + 3 = 21 - 3
18 = 18 (True statement).
Thus, the measure of each side of the triangle is 18, making the value of x = 3 as a valid answer.
