Question

if each angle of a triangle is less than the sum of the other two show that the triangle is acute angled

Answer 1

LET THE ANGLES BE A, B , C

IF EACH ANGLE IS LESS THAN OTHER TWO........

A < B+C
ADDING BOTH SIDES A

A +A <A + B + C
2 A < 180 (SUM OF ALL ANGLES IN A TRIANGLE =180 )

A < 180/ 2
A < 90

SIMILARLY WE CAN FIND ANGLE B AND C SMALLER THAN 90 DEGREE....
HENCE WE CAN PROVE THAT EACH ANGLE IS THAT THE SUM OF OTHER TWO...