Let the measures of the base angles be x, and the measure of the vertex angle be y.
y is bisected, and "each resulting angle is 51 degrees larger than a base angle"
y/2=x+ 51, thus y=2x+102°.
The measures of the interior angles are x-x-(2x+102)
The sum of the measures of the interior angles of any triangle is 180°, thus we have:
x+x+2x+102°=180°
4x=180°-102°
4x=78°
x=78°/4=19.5°
The measure of the obtuse angle is 2x+102°=2*19.5°+102°=141°
Answer: 141°
