An isosceles triangle has an angle that measures 40°. What measures are possible for the other two angles?

In an isosceles triangle, two angles are equal. If one of the angles measures 40°, then the other two angles, which must be equal, can be calculated as follows:

1. The sum of the angles in any triangle is 180°.
2. Subtract the known angle (40°) from 180°:

[

180° – 40° = 140°

]
3. Since the two equal angles are also part of the total, divide by 2:

[

140° / 2 = 70°

]

Therefore, the measures of the other two angles must be 70°.

So from your options, the possible measure for the other two angles is 70°.

To summarize:

– 70° is possible.

– 10°, 40°, and 100° are not possible as the other two angles in this scenario must equal 70° each.

In an isosceles triangle, two angles are equal. Since one angle measures 40°, the other two angles must be equal. Let’s denote the measure of the other two angles as ( x ).

According to the triangle sum property, the sum of the angles in a triangle is 180°. Therefore, we can set up the equation:

[ 40° + x + x = 180° ]

This simplifies to:

[ 40° + 2x = 180° ]

Subtracting 40° from both sides gives:

[ 2x = 140° ]

Now, dividing both sides by 2, we find:

[ x = 70° ]

So, the measures of the other two angles are both 70°. Among the options given, the only correct measure for the other two angles is:

70°.

This means the possible measures for the other two angles are 70°, and the other options (10°, 40°, and 100°) are not valid.