Question

An isosceles triangle has one angle measuring 26o. Which of the following could not be one of the other angle measures?
26o
64o
77o
128o

Answer 1

In an isosceles triangle, there are two equal angles. The sum of all angles in a triangle is always 180 degrees.

Given that one angle measures 26 degrees, we can denote the other two angles as \(x\). Therefore, the equation representing the sum of angles in this isosceles triangle is:

\[
26 + x + x = 180
\]

This simplifies to:

\[
26 + 2x = 180
\]
\[
2x = 180 - 26
\]
\[
2x = 154
\]
\[
x = 77
\]

Therefore, in this isosceles triangle, the two equal angles can both measure 77 degrees, and the other angle can measure 26 degrees.

Now let's evaluate the options:
- **26 degrees**: This could be an angle, as it is one of the angles specified.
- **64 degrees**: This cannot be an angle, as we already found the other angles must be 77 degrees or 26 degrees.
- **77 degrees**: This could be one of the angle measures, as we calculated it.
- **128 degrees**: This cannot be an angle, as the sum must equal 180 degrees, and having an angle of 128 degrees would not allow for two other angles that satisfy this condition.

Of the options provided, the only angle that **could not** be one of the other angle measures in the isosceles triangle is **64 degrees**.