One of two complementary angles is 4 degrees more than the other. Find the angles. (Recall that complementary angles are angles whose sum is 90 degrees.)
Which of the following equations can not be used to solve the problem if x represents one of the angles?
2x + 4 = 90
x + 4 = 90
2x - 4 = 90
x - 4 = 90
The correct equation that cannot be used to solve the problem if x represents one of the angles is 2x - 4 = 90.
To solve the problem, we need to set up an equation relating the two angles. Let's assume x represents one of the angles.
Since the two angles are complementary, the other angle can be represented as 90 - x.
Given that one angle is 4 degrees more than the other, we can set up the equation:
x = (90 - x) + 4
Simplifying this equation, we get:
2x = 94 - x
Now, let's analyze the options one by one:
1) 2x + 4 = 90: This equation can be used to solve the problem. We can solve for x by subtracting 4 from both sides and dividing by 2:
2x = 90 - 4
2x = 86
x = 43
2) x + 4 = 90: This equation can be used to solve the problem. We can solve for x by subtracting 4 from both sides:
x = 90 - 4
x = 86
3) 2x - 4 = 90: This equation cannot be used to solve the problem. Let's attempt to solve it anyway:
2x = 90 + 4
2x = 94
x = 47
As you can see, the value of x obtained from this equation is not consistent with the problem statement.
Therefore, the equation that cannot be used to solve the problem is 2x - 4 = 90.
To solve the problem, we need to find the two complementary angles. Let's represent one of the angles as x.
We know that one angle is 4 degrees more than the other. So, we can set up an equation based on this information.
Let's consider the options one by one:
1. 2x + 4 = 90: This equation can be used to solve the problem. We can solve it by subtracting 4 from both sides and then dividing by 2 to find the value of x.
2. x + 4 = 90: This equation can also be used to solve the problem. We can solve it by subtracting 4 from both sides to find the value of x.
3. 2x - 4 = 90: This equation cannot be used to solve the problem. If we set up this equation, we encounter a problem since the given condition is that one angle is 4 degrees more than the other. Here, 2x - 4 represents the difference between the two angles, not their relationship.
Therefore, the equation that cannot be used to solve the problem is 2x - 4 = 90.