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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The answer would be 37
To find the measure of angle PQM, we will use the properties of a rhombus.
In a rhombus, opposite angles are equal. So, angle MRQ is equal to angle PQM.
Given that the measure of angle MRQ is (13t - 1) degrees, we can set it equal to angle PQM.
13t - 1 = PQM.
Now, we are also given that the measure of angle PQR is (7t + 4) degrees.
In a rhombus, the sum of adjacent angles is 180 degrees. So, we can write an equation using the given angles:
PQM + PQR = 180.
Substituting the measure of angle PQR, we get:
PQM + (7t + 4) = 180.
Simplifying, we have:
PQM = 180 - (7t + 4).
PQM = 180 - 7t - 4.
PQM = 176 - 7t.
Therefore, the measure of angle PQM is 176 - 7t degrees.