SOLUTION: A triangle has 2 angles that each measure 45�. Which of the following best describes this triangle ? A. Obtuse Isosceles B. Equilateral C. Right Isosceles D. Right Scalene

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Question 709352: A triangle has 2 angles that each measure 45�. Which of the following best describes this triangle ?
A. Obtuse Isosceles
B. Equilateral
C. Right Isosceles
D. Right Scalene
Found 2 solutions by unlockmath, hheuler:
Answer by unlockmath(1688) (Show Source):
You can put this solution on YOUR website!
Hello,
C is the answer
RJ
www.math-unlock.com

Answer by hheuler(6) (Show Source):
You can put this solution on YOUR website!
We have two angles equal to each other so the triangle is possibly isosceles (it could be equilateral). It is not possible for the triangle to have three equal angles as their sum would only be 135 degrees (45 + 45 + 45). The sum of all three angles in any triangle is always 180 degrees, so this situation will not happen. So the triangle is not equilateral but isosceles. Answer B is not possible. Our triangle cannot be scalene (all sides different in length). We were given that two angles were equal in the triangle; this implies that the two sides opposite these two equal angles are also equal (by the property of an isosceles triangle). So Answer D is not correct.
Now, the sum of the two given angles is 90 degrees so the third unknown angle must be 180 - 90 = 90 degrees. This follows from the property of triangles that the sum of all three angles in any triangle is always equal to 180 degrees. So the triangle is right angled (one of the angles in the triangle is 90 degrees). So Answer C is correct.
Answer A is not correct as this statement requires that all sides have different lengths (a scalene triangle has three unequal sides and three unequal angles). This is not true as we are told that two of the given lengths are equal.
So the statement for Answer C best describes the given triangle.