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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Do you know the definition of an isosceles triangle?
yes
An isosceles triangle is a triangle that has at least two congruent sides. This means an isosceles triangle can have 2 congruent sides or 3 congruent sides.
In an isosceles triangle, the angles opposite the congruent sides are congruent.
|dw:1439395982729:dw|
If an isosceles triangle is also equilateral, then all angles are also congruent.
Let's look at an equilateral triangle first. Since you want one angle to measure 65 deg, then all angles would have to measure 65 degrees. This is a problem, because 65 + 65 + 65 > 180 and the sum of the measure of the angles of a triangle is 180, not more than 180. We now know we are not dealing with an equilateral triangle.
okay
This means we are dealing with an isosceles triangle with only two congruent sides and only two congruent angles.
Here is a case of an isosceles triangle having 2 65-deg angles. This is perfectly fine since 65 + 65 + 50 = 180. The top angle measures 50 degrees. |dw:1439396229682:dw|
okay
Now we know that at least one isosceles triangle with a 65-deg angle exists. The question we still have is whether there is another isosceles triangle with a 65-deg angle.
|dw:1439396409264:dw|
so it is A
What about the isosceles triangle above? It also has a 65-degree angle, but it's the vertex angle, not the base angles.
Correct.
thanks
You're welcome.

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