Chapter 2.8, Problem 13PSB

To determine

To Conclude about the two given angles.

Answer to Problem 13PSB

Angles will be right angles

Explanation of Solution

Given information :

A pair of vertical angles are supplementary

Formula used:

When two lines intersect each other and one pair of vertical angles are supplementary then second pair of vertical angles will also be supplementary

Two angles are said to be supplementary, if sum of these angles is $\text{180}°$

Proof:

Look at the fig (a)

Fig (a) Fig (b)

If two lines intersect each other at one point

Two pairs of vertically $\left(\angle \text{1\&}\angle \text{4 and}\angle 2\text{\&}\angle 3\right)$ are formed, i.e., four angles are formed

It is given that

A pair of vertical angles are supplementary

Now, look at fig(b),

If any of the pair of vertical angles are supplementary

Then other pair of vertical angles will automatically become supplementary

Thus, angles (vertical) forming supplementary angles will be right angles

Hence, we conclude at: angles will be right angles.