QRST is a trapezoid. If angle S is equal to 23 degrees, what is the measure of angle T
You did not state which sides are parallel, so we can't tell
If QT || RS, then obviously angle T = 180-23
T=157 degrees
To find the measure of angle T, we need to use the fact that the sum of the angles in a trapezoid is always equal to 360 degrees.
In a trapezoid, opposite angles are congruent. Therefore, angles S and T are opposite angles. So, if angle S is 23 degrees, then angle T is also 23 degrees.
To verify this, we can use the fact that the sum of the interior angles of a trapezoid is equal to 360 degrees:
Let's assume that angle R is equal to x degrees.
Angle Q and angle S are supplementary angles because they form a straight line. So, angle Q is equal to 180 degrees - angle S. Therefore, angle Q = 180 - 23 = 157 degrees.
The sum of the interior angles of a trapezoid is given by:
(x + Q) + (R + S) = 360 degrees
Substituting the known values:
(x + 157) + (x + 23) = 360
2x + 180 = 360
2x = 180
x = 90
Now we know that angle R is 90 degrees.
Since angles R and T are opposite angles, angle T in the trapezoid QRST is also 90 degrees.
Therefore, the measure of angle T is 90 degrees.