Pregunta
The measures of two angles of a triangle are given. Find the measure of the third angle. \( 47^{\circ}, 93^{\circ} \) The measure of the third angle is \( \square^{\circ} \). (Simplify your answer. Type an integer or a fraction.)
Ask by Hilton Wade. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The measure of the third angle is \(40^{\circ}\).
Solución
To find the measure of the third angle in a triangle where two angles are \(47^{\circ}\) and \(93^{\circ}\), you can use the fact that the sum of all interior angles in a triangle is \(180^{\circ}\).
\[
\text{Third angle} = 180^{\circ} - (47^{\circ} + 93^{\circ}) = 180^{\circ} - 140^{\circ} = 40^{\circ}
\]
**The measure of the third angle is \(40^{\circ}\).**
Answer: \(40\)
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Simplifique esta solución Extra Insights
The sum of the angles in a triangle is always \( 180^{\circ} \). So, to find the third angle, you can simply subtract the sum of the given angles from \( 180^{\circ} \). Here, \( 47^{\circ} + 93^{\circ} = 140^{\circ} \). Now, \( 180^{\circ} - 140^{\circ} = 40^{\circ} \). Therefore, the measure of the third angle is \( 40^{\circ} \). Feeling like a mathematician? Remember, every triangle tells a story with its angles! They're like characters in a play, and together, they must sum up to \( 180^{\circ} \), no exceptions! Keep this in mind, and you'll ace any triangle-related problem.
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