Question

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?

Answer 1

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°