Angles MRQ and RPN are alternate interior angles. If angle MRQ=5x+7 and angle RPN=7x-21, what is the value of x?
5x+7 = 7x-21
Alternate interior angles are equal when a transversal intersects two parallel lines. In this case, angles MRQ and RPN are alternate interior angles, so they must be equal:
5x + 7 = 7x - 21
To solve for x, we need to isolate it on one side of the equation. Let's start by subtracting 5x from both sides:
7 - 5x = 7x - 21 - 5x
Simplifying both sides:
7 - 5x = 2x - 21
Next, we can add 5x to both sides to further isolate x:
7 + 5x - 5x = 2x - 21 + 5x
Simplifying:
7 = 7x - 21
To isolate x, we can add 21 to both sides:
7 + 21 = 7x - 21 + 21
Simplifying:
28 = 7x
Finally, divide both sides by 7 to solve for x:
28/7 = 7x/7
Simplifying:
4 = x
Therefore, the value of x is 4.
To find the value of x, we need to set the two expressions for the angles equal to each other since they are alternate interior angles.
Given: Angle MRQ = 5x + 7 and Angle RPN = 7x - 21
Therefore, we can create an equation:
5x + 7 = 7x - 21
To solve this equation, we need to isolate the variable x. Let's start by getting rid of the terms with x on the right side of the equation.
To do this, we can subtract 5x from both sides of the equation:
5x - 5x + 7 = 7x - 5x - 21
Simplifying:
7 = 2x - 21
Next, let's isolate the variable x by getting rid of the constant term on the right side of the equation. We can do this by adding 21 to both sides:
7 + 21 = 2x - 21 + 21
Simplifying:
28 = 2x
Finally, to solve for x, we divide both sides of the equation by 2:
28 / 2 = 2x / 2
Simplifying:
14 = x
Therefore, the value of x is 14.