Question

The third angle in an isosceles triangle is 1/7 as large as each of the two base angles. Find the measure of each angle.

Answer 1

This is a systems problem.
They give you a couple of pieces of information to construct your system of equations.
First they tell you that the third angle (which I will call B) is 1/7 as large as each of the two base angles. Lets construct the first equation.

B=(1/7)A
(B is the third angle, A is the measure of the base angles.)
We know that triangles sum up to 180 degrees, which gives us our second equation, making our system look like this:

B=(1/7)A
A+A+B=180

Use the solved equation and put it into the second one.
A+A+(1/7)A=180
2A+(1/7)A=180
You want to group your A's together, so you must get a common denominator.
(14/7)A+(1/7)A=180
(15/7)A=180
Divide by (15/7), which is multiplying by (7/15).
A=180(7/15)
A=84
Now that you have a numerical value for A, use it in the simplest equation to find the numerical value of the other variable.
B=(1/7)A
B=(1/7)84
B=12

The solution, then, is A=84 and B=12.

Remember, isosceles means that two of the angles are the same measure.

Answer 2

thank you so much!!