Assertion : To construct an angle of` 45^(@)` we first draw angle of `90^(@)` and then bisect it using ruler and pair of compasses.
Reason : `45^(@)` is multiple of angle of `15^(@). `So, it can be drawn using ruler and pair of compasses.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To construct an angle of 45 degrees using a ruler and a pair of compasses, we can follow these steps:

### Step-by-Step Solution:

1. **Draw a Straight Line:**
- Start by drawing a straight horizontal line using a ruler. Label the endpoints as point A and point B.

**Hint:** Use a ruler to ensure the line is straight and long enough for your construction.

2. **Construct a 90-degree Angle:**
- At point A, use a compass to draw a circle with a radius that is convenient for you. The center of the circle will be point A.
- Mark the points where the circle intersects the line AB as points C and D.

**Hint:** The circle will help you find the points needed to create the right angle.

3. **Locate the 90-degree Angle:**
- Without changing the compass width, place the compass point at point C and draw an arc above the line.
- Now, keeping the same compass width, place the compass point at point D and draw another arc that intersects the first arc. Label the intersection point as point E.

**Hint:** Make sure the arcs intersect clearly to find point E accurately.

4. **Draw the 90-degree Angle:**
- Use a ruler to draw a straight line from point A through point E. This line forms a 90-degree angle with line AB.

**Hint:** Ensure that the line passes through point E to accurately represent the 90-degree angle.

5. **Bisect the 90-degree Angle:**
- Now, to bisect the angle AEB, keep the compass width the same and draw an arc from point E that intersects both lines AE and EB. Label the intersection points as F and G.
- Without changing the compass width, place the compass point at point F and draw an arc inside the angle.
- Then, place the compass point at point G and draw another arc that intersects the first arc. Label this intersection point as point H.

**Hint:** The intersection point H is crucial for finding the bisector of the angle.

6. **Draw the 45-degree Angle:**
- Finally, use a ruler to draw a straight line from point A through point H. This line represents the bisector of the 90-degree angle and thus creates a 45-degree angle with line AB.

**Hint:** Ensure the line passes through point H to accurately represent the 45-degree angle.

### Conclusion:
You have successfully constructed a 45-degree angle by first creating a 90-degree angle and then bisecting it.