An isosceles triangle has an angle that measures 112°. What measures are possible for the other two angles? Choose all that apply.
15°
44°
66°
34°
Possible Measures for Angles in an Isosceles Triangle with an Angle of 112°
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In an isosceles triangle, two angles are equal. Since the triangle has an angle measuring 112°, the sum of the other two angles must equal 68° (because the sum of all angles in a triangle is 180°).
Let’s denote the equal angles as x. We can set up the equation:
112° + x + x = 180°
112° + 2x = 180°
2x = 180° – 112°
2x = 68°
x = 34°
Thus, the measures of the other two angles in the triangle are both 34°.
From the options provided, the correct answer is 34°.
Keep in mind that the other angles listed (15°, 44°, 66°) do not make sense as they do not equal 34°. Great job considering the possibilities, and if you have more questions, feel free to ask! For more detailed help, check the extended services page.
In an isosceles triangle, two angles are equal, and the sum of all interior angles must equal 180°. Given that one angle measures 112°, the other two angles can be calculated as follows:
1. Start with the equation:
[
112° + 2x = 180°
]
where (x) is the measure of each of the equal angles.
2. Subtract 112° from both sides:
[
2x = 180° – 112° = 68°
]
3. Divide by 2 to find the measure of each angle:
[
x = frac{68°}{2} = 34°
]
Thus, the measures of the other two angles that are possible are both 34°. Therefore, the correct answer is:
34°
No other options (15°, 44°, 66°) would fit the requirements for the other two angles in this triangle. If you have more questions or need further assistance, feel free to ask for help!