Question

In the given figure, ∠1 and ∠2 are supplementary angles.

If ∠1 is decreased, what changes should take place in ∠2 so that both angles still remain supplementary.

Answer 1

Analyzing the figure:

Given:

In the figure, if the value of $\angle 1$decreases then the value $\angle 2$ has to increase for the angles to be supplementary because

$\angle 1+\angle 2=180°$

let the value to be decreased be $x$ and the value changed in $\angle 2$ as $y$

adding and subtracting $x$ to the equation

$$\begin{gathered} (\angle 1-x)+(\angle 2+y)=180° \\ \Rightarrow \angle 1+\angle 2-x+y=180° \\ \Rightarrow 180°-x+y=180° \\ \Rightarrow -x+y=0 \\ \Rightarrow x=y \end{gathered}$$

Therefore $\angle 2$ should increase with the same value

Hence, for both the angles to be supplementary, if the value of $\angle 1$ decreases then the value of $\angle 2$ will increase with the same value.