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.

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.

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