UPSC Prelims 1999 · General Studies

Question 141: Basic Numeracy

If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle

ais obtuse

bhas one angle greater than 80°

cis a right triangle

dis acute

AnswerThe answer is (d).

Angles in the ratio 4 : 3 : 2 make 9 parts = 180 degrees, so one part is 20 degrees and the angles are 80, 60 and 40 degrees. All are less than 90 degrees, so the triangle is acute. The largest angle is exactly 80 degrees, not more than 80. Remember: the angles add to 180 degrees; split them in the given ratio.

Why each option is right or wrong

(a) Wrong. An obtuse triangle needs an angle above 90 degrees.
(b) Wrong. The largest angle is exactly 80 degrees, not greater.
(c) Wrong. A right triangle needs a 90 degree angle.
(d) Right. All angles are below 90 degrees.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 1999, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.