MNPQ is a rhombus. The measure of angle MRQ is (13t-1) degrees, and the measure of angle PQR is (7t+4) degrees. what is the measure of angle PQM?
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Since MNPQ is a rhombus, opposite angles are equal. That means:
Angle MRQ = Angle PQR.
Given:
Angle MRQ = 13t - 1 degrees,
Angle PQR = 7t + 4 degrees.
Therefore, setting the two angles equal to each other:
13t - 1 = 7t + 4.
Simplifying the equation:
13t - 7t = 4 + 1,
6t = 5,
t = 5/6.
Now we can find the measure of angle PQR using the value of t:
Angle PQR = 7t + 4 = 7(5/6) + 4 = 35/6 + 24/6 = 59/6 degrees.
Since opposite angles of a rhombus are equal, the measure of angle PQM is also equal to the measure of angle PQR:
Angle PQM = Angle PQR = 59/6 degrees.
To find the measure of angle PQM in the rhombus MNPQ, we can use the fact that opposite angles in a rhombus are equal.
Since MNPQ is a rhombus, we know that angle MRQ is equal to angle PQM. Therefore, we need to find the value of angle MRQ.
Given that the measure of angle MRQ is (13t-1) degrees, we can set it equal to the measure of angle PQR, which is (7t+4) degrees:
13t - 1 = 7t + 4
Now we can solve this equation to find the value of t:
13t - 7t = 4 + 1
6t = 5
t = 5/6
Now that we have found the value of t, we can substitute it back into the expression for angle MRQ:
MRQ = 13t - 1 = 13(5/6) - 1 = 10.833 degrees
Since MRQ = PQM, the measure of angle PQM is also 10.833 degrees.