Pregunta
\( 2 x=30 \) b) If \( \angle 3=2 x+30 \) and \( \angle 5=3 x+100 \), find \( x \).
Ask by Collins Bradley. in the United States
Feb 26,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x = 15 \)
Solución
Solve the equation \( 2x=30 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(2x=30\)
- step1: Divide both sides:
\(\frac{2x}{2}=\frac{30}{2}\)
- step2: Divide the numbers:
\(x=15\)
It seems there was an issue with solving the system of equations directly. Let's try to solve it manually.
From the first equation:
\( \angle 3 = 2x + 30 \)
From the second equation:
\( \angle 5 = 3x + 100 \)
We can solve these equations manually to find the value of \( x \).
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Simplifique esta solución The Deep Dive
To solve for \( x \), first find \( x \) from the equation \( 2x = 30 \). Dividing both sides by 2 gives \( x = 15 \). Next, substitute \( x = 15 \) into the expressions for \( \angle 3 \) and \( \angle 5 \): - \( \angle 3 = 2(15) + 30 = 30 + 30 = 60^\circ \) - \( \angle 5 = 3(15) + 100 = 45 + 100 = 145^\circ \) Now that we have both angles, it's crucial to check whether they are related. If these angles are part of a linear pair, they should sum to \( 180^\circ \). Here, \( 60 + 145 = 205 \), which indicates they are not supplementary. Therefore, we’ve calculated correctly, but be sure to check the relationships between angles in geometry problems!
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