In a triangle abc , if 2 angle A = 3 angle B = 6 angle C , calculate the measures of angle A , angle B and angle C.
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In a triangle abc , if 2 angle A = 3 angle B = 6 angle C , calculate the measures of angle A ,
In a triangle abc , if 2 angle A = 3 angle B = 6 angle C , calculate the measures of angle A , angle B and angle C.
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Step-by-step explanation:
Let's denote the measures of angles A, B, and C as \(x\), \(y\), and \(z\) respectively.
According to the given information, we have the following relationships:
\[2x = 3y\]
\[3y = 6z\]
We can use these relationships to express \(x\) in terms of \(z\), and then find the values of \(x\), \(y\), and \(z\).
From the first relationship, we get \(x = \frac{3}{2}y\).
Then, substitute this into the second relationship:
\[3y = 6z\]
\[\frac{9}{2}y = 6z\]
\[y = \frac{4}{3}z\]
Now, we can find the values of the angles:
\[x = \frac{3}{2}y = \frac{3}{2} \times \frac{4}{3}z = 2z\]
\[y = \frac{4}{3}z\]
\[z = z\]
Therefore, the measures of the angles are:
Angle A (\(x\)) = \(2z\)
Angle B (\(y\)) = \(\frac{4}{3}z\)
Angle C (\(z\)) = \(z\)
Answer:
∠A=90degree,∠B=60degree,∠C=30degree.