Question

Angles A,B and C of a triangle satisfy B-A=30 and C-B=45. Find all the angles .

Answer 1

sum of angles in triangle = 180
A+B+C= 180
By given B-A =30
A=B-30
By given
C-B =45
C=45+B
Substituting these in A+B+C=180
B-30+B+45+B=180
3B=180-15
B=55
A=25
C=100

Answer 2

Heya,

Ur answer  is here.......


POINT TO REMEMBER :-

The sum of all angles of a triangle is 180°.
So, A + B + C = 180°.                         ........(i).

GIVEN :-
B - A = 30°
So, A = B - 30°.                         ................(ii).
Also, C - B = 45°
So, C = B + 45.                           ...............(iii).

From (i), (ii) and (iii), we get

(B - 30) + B + (B + 45) = 180
3B + 15 = 180
3 B = 165
Hence, B = 55°.

Now, A = B-30 = 25°.
and, C = B + 45 = 100°.
Hence, the three angles are 25°, 55° and 100°.

Let us do some verification :-

Angle Sum property of Triangles --
25° + 55° + 100° = 180°.

Next - B-A=30
55° - 25° = 30°.

Now, C-B=45.
100° - 55 = 45°.

Hence, verified.

Hope this answer helps uhh