Question

In ΔABC, $A+B= 70^o$ and $B+C = 135^o$. Find the measure of each angle of the triangle.

Answer 1

A+B=70^o  B+C=135^o  add both equations then we get A+2B+C=205 but we know that A+B+C =180^o  by solving these to we get B=25^o then A=70-25=45  and C=135-25=110 

Answer 2

A+B=70^o..................(i)
B+C=135^o................(ii)
Adding equation (i) and (ii),
A + B + B + C = 70^o + 135^o
A + 2 B + C = 205^o.....(iii)
As we know that sum of all angles of a triangle is 180^o,
Thus,
A + B + C = 180^o.......(iv)
Substracting equation (iii) and (iv),
A + 2 B + C - A - B - C = 205^o - 180^o
Therefore, B = 25^o
Substituting the value of B in equation (i) & (ii),
A + B = 70^o ⇒ A + 25^o = 70^o ⇒ A = 70^o - 25^o ⇒ A = 45^o
B + C = 135^o ⇒ 25^o + C = 135^o ⇒ C = 135^o - 25^o ⇒ C = 110^o
Therefore,
A = 45^o
B = 25^o
C = 110^o