The sum of the angles in a triangle is 180°. By taking 180 and subtracting the two angles that you are given (55° and 55°), the third angle is 70°. From the question you are given, we also know that two sides of the triangle have an equal length. Let's analyze your answer choices:
A. acute isosceles
Acute angles are those that are less than 90°. An isosceles triangle has at least two equal sides. For a triangle to be acute isosceles, it would need at least two equal sides with all angles less than 90°.
B. right scalene
Scalene triangles have three sides that are not equal. Right scalene triangles have a right angle (90° angle) in them. Considering you do not have a right angle and two sides that are of the same length, your triangle is not right scalene.
C. acute scalene
An acute scalene triangle has three sides that are not equal with all angles less than 90°. Although your triangle has angles less than 90°, it cannot be scalene because it has two sides that are the same length.
D. obtuse isosceles
Again, an isosceles triangle has at least two equal sides. However, an obtuse isosceles triangle has an angle that is more than 90°. There is not an obtuse angle present in your triangle, so it is not obtuse isosceles.
Based on these properties, the correct answer would be A. acute isosceles due to its 3 acute angles and at least two equal sides.
