Determine if the given conjecture is true or not. Give a counterexample if it is false.
Given: ∠𝑃 𝑎𝑛𝑑 ∠𝑄 are complementary. ∠𝑄 𝑎𝑛𝑑 ∠𝑅 are complementary.
Conjecture: ∠𝑃 ≅ ∠𝑅

The correct answer is: the given conjecture is true

We have given that

            ∠𝑃 𝑎𝑛𝑑 ∠𝑄 are complementary.

 ∠𝑄 𝑎𝑛𝑑 ∠𝑅 are complementary.
Which means ∠𝑃 + ∠𝑄 = 90
And  ∠𝑄 + ∠𝑅 = 90
If we subtract ∠𝑄 from both sides of both equations we get,

∠P  =90 - ∠𝑄

∠R = 90 - ∠𝑄
If we compare RHS of the both obtained equations
We can say that

∠𝑃 ≅ ∠𝑅
Therefore, the given conjecture is true.