In the given parallelogram QRST the measure of angle T would be 80 degrees.
The correct answer is option 3.
In the given figure we are a parallelogram QRST.
In the parallelogram QRST a diagonal is drawn Qs as we can see it in the given figure.
We need to find the value of angle T.
So , in order to find the value of angle T first we would find the value of angle R because angle R would be equal to angle T as opposite angles of parallelogram are equal .
As we can see in the figure the diagonal has made a triangle named QRS where Q measures 66 degrees and S measures 34 degrees .
Now by using angle sum property of a triangle which states that the sum of measures of all angles of a triangle is going to equal to 180 degrees.
So in triangle QRS we can use angle sum property to find the value of R.
66 + x + 34 = 180 ( assumed angle R as x )
100 + x = 180
x = 180 - 100
x = 80
So , the measure of angle R would be 80 degrees.
As we have stated above that angle R would be equal to angle T as they both are opposite angles of a parallelogram.
So angle T = 80 degrees.
Therefore , from the given options the correct one is option 3.