An isosceles triangle has an interior angle of 26 degrees. Which of the following is a possible degree measure for one of the other interior angles of the triangle?
a) 52 degrees
b) 64 degrees
c) 78 degrees
d) 104 degrees
e) 128 degrees
The answer should be c). The sum of angles for a triangle is 180 degrees. Since this is an isosceles triangle, it must have two equivalent angles. Therefore 180-26 = 154 degrees. When we divide 154 by 2, we get 77 degrees. So the possible degree measure is 78.
To find the measure of the other interior angles of an isosceles triangle, you need to know that an isosceles triangle has two congruent (equal) angles. In this case, one of the interior angles is given as 26 degrees.
Let's assume the other congruent angle is x degrees.
Since the sum of the interior angles of any triangle is always 180 degrees, we can set up the following equation:
26 + x + x = 180
Simplifying the equation:
26 + 2x = 180
Subtracting 26 from both sides:
2x = 154
Dividing both sides by 2:
x = 77
Therefore, the other congruent angle of the isosceles triangle is 77 degrees.
Now, let's check the answer choices:
a) 52 degrees: This is NOT a possible measure for the other interior angle.
b) 64 degrees: This is NOT a possible measure for the other interior angle.
c) 78 degrees: This is NOT a possible measure for the other interior angle.
d) 104 degrees: This is NOT a possible measure for the other interior angle.
e) 128 degrees: This is NOT a possible measure for the other interior angle.
Therefore, none of the given answer choices is the possible degree measure for one of the other interior angles of the isosceles triangle.