Given that $s$ is an acute angle and $PR \parallel QT$, compare the following quantities:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756842243/aptidude_questions/z7dxrurum0eitb8j5xmn.png)

Which of the following is true?

Question

Given that $s$ is an acute angle and $PR \parallel QT$, compare the following quantities:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756842243/aptidude_questions/z7dxrurum0eitb8j5xmn.png)

Which of the following is true?

Accepted Answer

**Solution:**

1. Since $s$ is an acute angle, we know that $s < 90^\circ$.

2. Given that $PR \parallel QT$, the angles $(a + 40)^\circ$ and $a^\circ$ are related such that their sum is less than $90^\circ$ because $s$ is acute.

3. Therefore, we write the inequality:
   $$ (a + 40) + a < 90 $$

4. Simplifying:
   $$ 2a + 40 < 90 $$
   $$ 2a < 50 $$
   $$ a < 25^\circ $$

5. Comparing Quantity I ($a$) and Quantity II ($25^\circ$), we find:
   $$ a < 25^\circ $$

**Answer:** Quantity I $<$ Quantity II

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