SOLUTION: Each of the equal angles of an isosceles triangle is four times as large as the third angle? What is the measure of each equal angle? What is the measure of the third

Algebra ->  Triangles -> SOLUTION: Each of the equal angles of an isosceles triangle is four times as large as the third angle? What is the measure of each equal angle? What is the measure of the third       Log On


   



Question 1154040:
Each of the equal angles of an isosceles triangle is four times as large as the third angle?
What is the measure of each equal angle?
What is the measure of the third angle?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Each of the equal angles of an isosceles triangle is four times as large as the third angle?
What is the measure of each equal angle?
What is the measure of the third angle?
an isosceles triangle is a triangle that has two sides of equal length
both base angles are equal, alpha=beta
if each of the equal angles of an isosceles triangle is four times as large as and the third angle gamma, we have
alpha=4gamma....eq.1
beta=4gamma.....eq.2
the sum of all angles is 180
so, alpha%2Bbeta%2Bgamma=180....eq.3
substitute alpha and beta+from+eq.1+and+eq.2%0D%0A%0D%0A%7B%7B%7B4gamma%2B4gamma%2Bgamma=180
9gamma=180
gamma=180%2F9
gamma=20=> the measure of the third angle

the measure of each equal angle:
then alpha=4%2A20=>alpha=80 and beta=80