if angle S and angle T are complimentry and angle T and angle U are supplementry, then angle U is an ____________ angle. What kind of angle?
==> S and T are complimentary angles.
==> A+T = 90 degrees............(1)
==> T and U are supplementary angles.
==> U + T = 180 degrees............(2)
We will subtract (1) from (2).
==> U-A = 90 degrees.
==> U = 90+A
Then we conclude that U is an angle greater than 90 but less than 180 since A can not be greater than 90 because it is a complement angle for T.
Since U is greater that 90 degrees and less than 180, then U is an OBTUSE angle.