the measure of angles of triangle are in A.P. and greatest is 5times the smallest find the angles in degree &radian
From angle, sum property we know that sum of internal angles of a triangle is equal to 180°.
Considering it to be in A.P . let us assume first angle to be ‘a’ and smallest and now according to the question, the third and the largest is 5a . Now , let the second angle be equal to a+d , where ‘d’ is the common difference term of an AP. Using the properties of an AP , we get that , [(a+d) – (a)] = [5a - (a +d)]
[Property used: If X Y Z are in AP then Y – X = Z – Y ]
This gives , d = 4a -d ------ (1)
Also , a + (4a-d) + a + 5a = 180
11a - d = 180 --------- (2)
From 1 , d = 2a .
putting this in 2 .
a = 20 °.
d = 40°
So angles respectively will be 20 ° , 60° and 100°. Now these can be converted into radians by multiplying them by 0.0174.
Good Luck
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