Chapter 3.5, Problem 52SPR

To determine

Give counter example to show that the given conjecture is false.

Explanation of Solution

Given :

  $\angle 1\text{ and }\angle \text{2}$ are complementary angles.

Conjecture : $\angle 1\text{ and }\angle \text{2}$ form a right angle.

Calculation :

Counter example , since the conjecture is false.

Consider the diagram:

  

Here , let $m\angle 1\text{ =}m\angle \text{2}=45°$ .

So, $m\angle 1\text{ + }m\angle \text{2}=\text{90}°$ . Hence $\angle 1\text{ and }\angle \text{2}$ are complementary angles , since their sum is $\text{90}°$ .

But they do not form a right angle, they are vertically opposite angles.