Question

In $\Delta ABC,\angle A + \angle C = {110^0},\angle B + \angle C = {145^0}$ then Find $\angle A,\angle B,\angle C$.

Answer 1

Hint: As we know that the sum of angles in the triangle is {180^0}. So use this condition and substitute the given value, we will get the answer.

Complete step-by-step answer:
Given,
$\angle A + \angle C = {110^0}..........(i)$
$\angle B + \angle C = {145^0}..........(ii)$
We know, the sum of three angles of a triangle is ${180^0}$.
$
  \therefore \angle A + \angle B + \angle C = {180^0} \\
  \angle A + {145^0} = {180^0} \\
  \angle A = {180^0} - {145^0} \\
  \angle A = {35^0} \\
$ [ Given data i.e. from equation (ii)]
Using equation $(i)$
$
  \angle A + \angle C = {110^0} \\
   \Rightarrow {35^0} + \angle C = {110^0} \\
   \Rightarrow \angle C = {110^0} - {35^0} \\
   \Rightarrow \angle C = {75^0} \\
$
Using equation $(ii)$
$
  \angle B + \angle C = {145^0} \\
   \Rightarrow \angle B + {75^0} = {145^0} \\
   \Rightarrow \angle B = {145^0} - {75^0} \\
   \Rightarrow \angle B = {70^0} \\
$
Hence, The value of $\angle A,\angle B$ and $\angle C$ are ${35^0}, {70^0}$ and ${75^0}$ respectively.

Note: To solve this question we used the sum of three angles as an equation and by the method of substitution we get our answer.