Using a ruler and a pair of compasses only construct angle ABC such that[AB]=10cm,angle ABC=30°and angle BAC=45°.A perpendicular from C to AB at D.Measure[CD]

Answer 1

Step 1: Draw a line segment AB of length 10 cm using the ruler.

Step 2: Draw a ray AC at an angle of 45 degrees to AB using the compasses. Place the tip of the compasses at point A and draw an arc that intersects AB. Without changing the width of the compasses, place the tip at the intersection point and draw another arc that intersects the first arc. This creates an angle of 45 degrees.

Step 3: Draw a ray BD at an angle of 30 degrees to AB using the compasses. Place the tip of the compasses at point B and draw an arc that intersects AB. Without changing the width of the compasses, place the tip at the intersection point and draw another arc that intersects the first arc. Draw a ray from B that passes through the intersection point and label it as BD.

Step 4: Construct a perpendicular from point C to AB. Place the tip of the compasses at point C and draw an arc that intersects AC and BD. Without changing the width of the compasses, place the tip at the intersection point and draw another arc that intersects the first arc. Draw a line segment from C to the intersection point on AB, label the intersection point as D.

Step 5: Measure CD using the ruler.