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Question
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Solution
\[a - d + a + a + d = 180 \left[ angle sum property \right]\]
\[ \Rightarrow 3a = 180\]
\[ \Rightarrow a = 60\]
\[Now, \left( a + d \right) = 2\left( a - d \right)\]
\[ \Rightarrow a + d = 2a - 2d\]
\[ \Rightarrow a = 3d\]
\[ \Rightarrow d = \frac{60}{3} = 20\]
\[\text{ Therefore, the three angles of a triangle are 40, 60, 80 } .\]
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