Final answer:
The value of x can be found by setting m∠2 and m∠4 equal to each other, then solving the resulting equation. Subtracting 2x from both sides and then adding 40 to both sides reveals that the value of x is 45.
Step-by-step explanation:
To find the value of x, we can set the two angles equal to each other: (2x + 5) = (3x - 40). Now, we can solve for x: 2x + 5 = 3x - 40. 40 + 5 = 3x - 2x. 45 = x.
When solving for the value of x given that m∠2 = (2x + 5) and m∠4 = (3x – 40), we initially don't have any additional information about the relationship between the angles. However, if we assume that m∠2 and m∠4 are equal (which is commonly the case in problems requiring you to solve for variables in angle expressions), we create an equation by setting them equal to one another:
To solve for x, we'll rearrange the equation to isolate x:
- Subtract 2x from both sides to get x on one side of the equation:
- 5 = x – 40
- Add 40 to both sides to solve for x:
- 45 = x
Therefore, the value of x is 45.