Question

How do you solve for b in $a+b+c=180$?

Answer 1

Hint: The given equation is a simple linear equation in terms of three numbers a, b and c, which is written in the above question as $a+b+c=180$. The above question tells us to solve the given equation of b. This means that we need to treat b as a variable, while the other numbers a, and b as constants. Therefore, we need to obtain b in terms of the numbers a, and b. For obtaining this, we first have to subtract a from both the sides of the given equation. Then, on subtracting c from both the sides of the obtained equation, we will finally obtain b in terms of a and c which will be the final solution of the given equation.

Complete step-by-step answer:
The equation given in the above question is written as
$\Rightarrow a+b+c=180$
The above question is directing us to solve the given equation for b. This means that b has to be treated as a variable, while the other numbers a, and b are to be treated as constants. So effectively, we need to obtain the value of b in terms of a and c. Therefore, we subtract a from both the sides of the above equation to get
$\begin{align}
  & \Rightarrow a+b+c-a=180-a \\
 & \Rightarrow b+c=180-a \\
\end{align}$
Now, we subtract $c$ from both sides of the above equation to finally get
$\begin{align}
  & \Rightarrow b+c-c=180-a-c \\
 & \Rightarrow b=180-\left( a+c \right) \\
\end{align}$
Hence, the value of b is obtained as $180-\left( a+c \right)$.

Note: Although it is not mentioned in the question which is a constant or a variable out of a, b and c, it is convenient to choose the one, which we need to obtain the value for, as the variable. We can also subtract $\left( a+c \right)$ from the given equation to get the solution in a single step.