Draw an angle of 152° and divide it into four equal parts.

Steps:

1. Draw a ray OA.

2. Place the centre of the protractor at O and the zero line along OA. Mark a point at 152°.

3. Remove the protractor and join O with the marked point and produce it to B. Then ∠AOB = 152°.

4. With O as centre and any (suitable) radius, draw an arc to meet ray OA at C and ray OB at D.

5. With C and D as centres, draw arcs of equal radius $\left(\gt\dfrac{1}{2}\text{CD}\right)$ cutting each other at E. Join OE and produce it. Then OE bisects ∠AOB, so ∠AOE = ∠EOB = 76°.

6. Let OE meet the first arc at point F.

7. Now bisect ∠AOE: with C and F as centres, draw arcs of equal radius cutting each other at G. Join OG and produce it.

8. Similarly, bisect ∠EOB: with F and D as centres, draw arcs of equal radius cutting each other at H. Join OH and produce it.

Then OG bisects ∠AOE and OH bisects ∠EOB.

Therefore, ∠AOG = ∠GOE = ∠EOH = ∠HOB = 38°.

and ∠AOE = ∠AOG + ∠GOE = 76°

∠EOB = ∠EOH + ∠HOB = 76°

Hence, the angle of 152° is divided into four equal parts each of measure 38°.