Question
\( \begin{array}{ll}43 & \text { Dati } \\ \widehat{B}-\widehat{C}=43^{\circ} & \widehat{A}=\text { ? } \widehat{B}=\text { ? } \widehat{C}=\text { ? } \\ \widehat{B}+\widehat{C}=143^{\circ} & \end{array} \)
Ask by Elliott Fernandez.
Nov 25,2024 14:36
UpStudy AI Solution
Tutor-Verified Answer
Answer
\[
\widehat{A} = 37^\circ, \quad \widehat{B} = 93^\circ, \quad \widehat{C} = 50^\circ
\]
Solution
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Mind Expander
Let's solve the angles step by step!
We know that \( \widehat{B} - \widehat{C} = 43^{\circ} \) and \( \widehat{B} + \widehat{C} = 143^{\circ} \). We can set up a system of equations.
1. From \( \widehat{B} + \widehat{C} = 143^{\circ} \):
Let's say \( \widehat{C} = \widehat{B} - 43^{\circ} \).
2. Substitute this into the second equation:
\[ \widehat{B} + (\widehat{B} - 43) = 143 \]
\[ 2\widehat{B} - 43 = 143 \]
\[ 2\widehat{B} = 186 \]
\[ \widehat{B} = 93^{\circ} \].
3. Now, substituting back to find \( \widehat{C} \):
\[ \widehat{C} = 93 - 43 = 50^{\circ} \].
4. We can now find \( \widehat{A} \) using the fact that the sum of angles in a triangle is \( 180^{\circ} \):
\[ \widehat{A} + \widehat{B} + \widehat{C} = 180 \]
\[ \widehat{A} + 93 + 50 = 180 \]
\[ \widehat{A} = 180 - 143 = 37^{\circ} \].
In conclusion, the angles are:
\( \widehat{A} = 37^{\circ} \), \( \widehat{B} = 93^{\circ} \), \( \widehat{C} = 50^{\circ} \).
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