Question

In the figure given, $\angle XOZ$and $\angle YOZ$ form a linear pair. If $p-q=80$, what are the respective values of p and q?

Answer 1

Hint: We have $\angle XOZ=p$ and $\angle YOZ=q$. Since $\angle XOZ$and $\angle YOZ$ form a linear pair, therefore, $\angle XOZ+\angle YOZ={{180}^{\circ }}$. It is also given that $p-q=80$. So, we have two equations in two variables. Solve the set of equations to get the value of p and q.

Complete step by step answer:
As we know that $\angle XOZ$and $\angle YOZ$ form a linear pair, therefore,
$\angle XOZ+\angle YOZ={{180}^{\circ }}......(1)$
Also, we have: $\angle XOZ=p$ and $\angle YOZ=q$
So, we can write equation (1) as:
$p+q={{180}^{\circ }}......(2)$
It is also given that $p-q=80......(3)$
So, we have two equations in two variables.
Now, to solve both the equations, subtract equation (3) from equation (2), we get:
$\begin{align}
  & \Rightarrow 2q={{100}^{\circ }} \\
 & \Rightarrow q={{50}^{\circ }}......(4) \\
\end{align}$
Now, put value of q from equation (4) in equation (3), we get:
$\begin{align}
  & \Rightarrow p-{{50}^{\circ }}={{80}^{\circ }} \\
 & \Rightarrow p={{130}^{\circ }}......(5) \\
\end{align}$

Hence, value of p and q is ${{130}^{\circ }}$ and ${{50}^{\circ }}$ respectively.

Note: The sum of angles making a linear pair is ${{180}^{\circ }}$ while the sum of angles around a point is ${{360}^{\circ }}$.
Also, while solving the linear equations in two variables, you can use either elimination method or substitution method to get the value of p and q.