Question

angle of a triangle are in Ap the greatest angle is twice the leasr find all the angles of triangle

Answer 1

The angles of the Triangle are as follows :-
40 degrees, 60 degrees, 80 degrees.


Please refer the above photograph for the used process.


KEY POINTS TO REMEMBER :-

☸️ AP stands for Arithmetic Progression.


☸️ If the given observations are in AP, their form must be as follows :-

a, a+d, a+2d, a+3d .......... , a+(n-1)d


☸️ Where a is the first term of AP and d is the common difference between the terms of AP.

Common difference is equal to
$(t\frac{}{2}) -( t\frac{}{1} )$
Where t2 and t1 are the second and first terms of AP respectively.


☸️ In the question, there is a triangle. This means there are three angles and hence here the AP consists of only 3 terms.
Also, it is given that the last (greatest angle) term is twice the first (smallest angle) terms of the AP.

So,
In equational form, we can express :-

$2a = a + 2d$

And from here normal calculation is continued to find the values of 'a' and 'd' of the AP.
(As shown in the attachment)


Thanks!