SOLUTION: Hello. I have an assignment but I don't know how to solve some of these word problems (that are algebraic equations by the way) but I already know the answers by guess and check. O

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Question 792097: Hello. I have an assignment but I don't know how to solve some of these word problems (that are algebraic equations by the way) but I already know the answers by guess and check. Okay so "A family of Isosceles triangles has the property that the two equal angles are each 2/15 of the angle. Find the measure of all 3 angles" so the equation I think would be 180=x(times) 2/15. the angles are 19,19, and 142 but I don't know how to show it. :)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The two equal angles (the base angles) are each 2/15 of what angle?
A straight angle (a 180%5Eo angle)?
The vertex angle of the isosceles triangle?

OPTION 1:
If each the base angles measures 2%2F15 as much as a straight angle, we do not even need an equation to find the measure of those angles. The measure of each base angle would be
180%5Eo+%2A%282%2F15%29=24%5Eo.
Then, if we can call the measure of the remaining angle x.
42%5Eo%2B42%5Eo%2Bx=180%5Eo
84%5Eo%2Bx=180%5Eo
x=180%5Eo-84%5Eo
x=96%5Eo

OPTION 2:
If each the base angles measures 2%2F15 as much as the vertex angle, the measures are not going to be whole numbers.

x= measure of the vertex angle of the isosceles triangle (in degrees)

The summ of the measures of the angles in any triangle is 180%5Eo, so
%282%2F15%29x%2B%282%2F15%29x%2Bx=180 is our equation.

Simplifying and solving:
%282%2F15%29x%2B%282%2F15%29x%2Bx=180
%282%2F15%29x%2B%282%2F15%29x%2B1%2Ax=180
%282%2F15%2B2%2F15%2B1%29x=180
%282%2F15%2B2%2F15%2B15%2F15%29x=180
%28%282%2B2%2B15%29%2F15%29x=180
%2819%2F15%29x=180
Multiplying times 15 both sides of the equal sign, we get
19x=180%2A15
19x=2700
x=2700%2F19 (about 142.1%5Eo)
Then, each of the other two angles would measure
%282%2F15%29%282700%2F19%29=2%2A2700%2F%2815%2A19%29=36%2F19 (about 18.95%5Eo)