Draw an angle of 80° using a protractor and divide it into four equal parts, using ruler and compasses. Check your construction by measurement.
Construction: (1) Draw 80°. (2) Bisect to 40°. (3) Bisect each 40° again to obtain four equal 20° angles. Verify with protractor.
You will need: a ruler (scale), a compass, a sharp pencil, and a protractor.
Step 1 — Draw the base line.
Draw a straight line and mark a point O on it. This line will be one arm of the angle.
Step 2 — Make an 80° angle with a protractor.
Place the protractor on point O, with the baseline along your line.
Mark a point at (80^circ).
Remove the protractor and join point O to the mark. You now have angle (angle AOB = 80^circ).
Step 3 — Bisect the 80° angle to get 40°.
With the compass on O, draw an arc that cuts both arms of the angle at points P and Q.
Without changing the compass width, draw an arc from P inside the angle.
With the same width, draw another arc from Q to meet the previous arc at R.
Draw a ray from O through R. This ray is the bisector.
Now the angle is split into two equal parts:
(80^circ = 40^circ + 40^circ)
Step 4 — Bisect each 40° again to make four equal parts.
Repeat the same bisection method on the left 40° part to get two angles of
(20^circ)
Repeat on the right 40° part to get two more angles of
(20^circ)
Finally, the whole 80° is divided into four equal angles:
(80^circ = 20^circ + 20^circ + 20^circ + 20^circ)
Why this works (in simple words):
An angle bisector always cuts an angle into two equal angles. If we keep bisecting, we keep halving the size.
(80^circ o 40^circ o 20^circ)
Check your construction with a protractor:
Measure each small angle. Each one should be about
(20^circ)
Small 1–2° differences can happen due to drawing or reading errors. Try to be neat for better accuracy.
Neatness tips:
Answer: The 80° angle is divided into four equal angles of 20° each. This is confirmed by measurement.