The angles of a triangle are in the ratio 1:3:5. Find the measure of each angle.

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Solution

Dear Student,

$W e a r e g i v e n t h a t t h e a n g l e s o f t h e t r i a n g l e a r e i n t h e r a t i o o f 1 : 3 : 5 . L e t t h e a n g l e s b e x, 3 x a n d 5 x . ∴ x + 3 x + 5 x = 180 ° [A n g l e s u m p r o p e r t y o f a t r i a n g l e] \Rightarrow 9 x = 180 ° \Rightarrow x = \frac{180}{9} = 20 ° T h u s, x = 20 °, 3 x = 3 \times 20 ° = 60 ° a n d 5 x = 5 \times 20 ° = 100 ° a r e t h e m e a s u r e s o f t h e t h r e e a n g l e s .$

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