The angles of a triangle are in the ration 3 : 5 : 7. The triangle is
(a) acute-angled
(b) obtuse-angled
(c) right-angled
(d) an isosceles triangle

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Solution

(a) acute-angled

Let the angles measure $(3 x) °, (5 x) ° and (7 x) °$ .
Then,
$3 x + 5 x + 7 x = 180 ° \Rightarrow 15 x = 180 ° \Rightarrow x = 12 °$
Therefore, the angles are $3 (12) ° = 36 °, 5 (12) ° = 60 ° and 7 (12) ° = 84 °$ .
Hence, the triangle is acute-angled.

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