One angle of an isosceles triangle measures 80°. What measures are possible for the other two angles? Choose all that apply.
50°
80°
38°
20°
One angle of an isosceles triangle measures 80°. What measures are possible for the other two angles?
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In an isosceles triangle, two angles are equal. If one angle measures 80°, it means the other two angles need to add up to 100° (since the total in a triangle is 180°).
The two equal angles can either both be:
– If they are both 80°, then it cannot work since the third angle would be 20°.
– If they are both equal to a number that, when added to 80°, equals 180°.
The only possibility left would be 50° because:
– Two angles of 50° each give us 100° plus the 80° makes 180°.
So the possible measures for the other two angles are:
– 50°
Therefore, the possible answer is: 50°.
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In an isosceles triangle, two angles are equal. Given that one angle measures 80°, the other two angles must be the same. The sum of all angles in a triangle is always 180°.
Let’s denote the two equal angles as ( x ). So we can set up the equation:
[ 80° + x + x = 180° ]
This simplifies to:
[ 80° + 2x = 180° ]
Now, subtract 80° from both sides:
[ 2x = 100° ]
Next, divide by 2:
[ x = 50° ]
So, the two equal angles must both measure 50°. Therefore, the possible measures for the other two angles are:
– 50° (correct)
The other options (80°, 38°, and 20°) do not apply as the angles of an isosceles triangle in this scenario.
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