angles MRQ and RPN are alternate interior angles. If angle MRQ=5x+7 and angle RPN=7x-21, what is the value for angle MRQ?
the two angles are equal, so just set them equal and solve for x
Then figure MRQ
angles mrq and Rpn are alternate interior angles. if angle mrq =5x+7 and angle rpn = 7x-21, what is the value for angle mrq
14
To find the value of angle MRQ, we need to set up an equation based on the given information that angles MRQ and RPN are alternate interior angles.
Alternate interior angles are formed when a transversal line intersects two parallel lines. In this case, the transversal line could be either MR or RN, and the parallel lines would be PQ and MN.
Since angles MRQ and RPN are alternate interior angles, they are congruent, meaning they have the same measure. Therefore, we can set up the equation:
5x + 7 = 7x - 21
Now we can solve the equation to find the value of x and then substitute it back into the expression for angle MRQ to find its value.
5x + 7 = 7x - 21
To solve this equation, we can start by isolating the variable terms (those with x) on one side and the constant terms (those without x) on the other side:
7 + 21 = 7x - 5x
28 = 2x
Next, we can isolate the variable x by dividing both sides of the equation by 2:
28/2 = x
14 = x
Now that we have the value of x, we can substitute it back into the expression for angle MRQ:
angle MRQ = 5x + 7
= 5(14) + 7
= 70 + 7
= 77
Therefore, the value of angle MRQ is 77.