Nat222: the obtuse angle of an isosceles triangle is bisected, and each resulting angle is 51 degrees larger than a base angle. how many degrees are in the measure of the obtuse angle?

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°

141°