Question

One of the angles of a triangle is 55 . Find the remaining two angles if their differnce is 35.

Answer 1

Heya ......

Given :-

It is given that  one angle is 55°. Also the difference between the remaining two sides are 35°. 
 
So, x - y = 35°.         .............(i)
 

We all know that the sum of angles of a triangle is 180°.

Let the other two angles be x and y.

ATQ, 

55 + x + y = 180.
-> x + y = 180 - 55
-> x + y = 125.                    ........(ii)

Adding eq. (i) and (ii), we get 

                        x     +      y       =   125
                        x      -      y       =     35
              ------------------------------------------------
                       2x                     = 160.

Hence, x = 80.

Putting x = 80 in eq. (i), we get

80 - y = 35.
-y = 35 - 80
y = 45.

Hence, the values of x and y are 80 and 45 respectively. So, the other two angles are 80° and 45°.

Let us verify ________

Sum of angles = 55° + 80° + 45° = 180°.

Hence, the sum of angles is 180°.

Also, 
x - y = 80 - 45 = 35°.

Hence, Verified.........

Hope it helps............