An isosceles triangle has an angle that measures 40°. What measures are possible for the other two angles? Choose all that apply.
70°
10°
40°
100°
An isosceles triangle has an angle that measures 40°. What measures are possible for the other two angles?
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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.