Question

10. In an acute angled triangle where the angles are all
natural numbers, 15 times an angle equals 17 times
one of the other angles. What is the measure of the
largest possible angle in the triangle?
(A) 75° (B) 76°
(C) 85° (D) 84°

Answer 1

Answer:

85 is the correct answer

Answer 2

Given :    In an acute angled triangle where the angles are all natural numbers, 15 times an angle equals 17 times one of the other angles.

To find :  What is the measure of the largest possible angle in the triangle  

(A) 75° (B) 76°

(C) 85° (D) 84°

Solution:

A + B + C = 180°

15A  = 17B

A can be  17  34  51  68  85   as A  <  90°

then B      15  30  45  60  75  

A + B  ≥ 90°  as  C < 90°

(A , B)   (51 °, 45°)  , ( 68° , 60° ) and ( 85° , 75°)

C =           84°                52°                    20°      

Largest     84°               68°                   85°

in all these 3 ,  85° is largest

Hence  largest possible angle in the triangle =     85°

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