Question

How to construct the angle $75°$?

Answer 1

Steps of construction:

Step 1: Draw a line segment with endpoints $\mathrm{O}$ and $\mathrm{A}$.

Step 2: Draw a semi-circle with some radius with $\mathrm{O}$ as center cutting the line segment $\mathrm{OA}$ at point $\mathrm{B}$ with a compass.

Step 3: Keeping the radius same, draw an arc with $\mathrm{B}$ as center cutting the semicircle at $\mathrm{C}$.

Step 4: Keeping the radius same, and $\mathrm{C}$ as the center, draw an arc intersecting the semicircle at $\mathrm{D}$.

Step 5: With any radius, draw two arcs with $\mathrm{C}$ and $\mathrm{D}$ as a center which intersect these two arcs at $\mathrm{E}$.

Step 6: Join $\mathrm{OE}$, $\angle \mathrm{EOA}$ is the angle with measurement of $90°$.

Step 7: Taking $\mathrm{E}$ and $\mathrm{C}$ as a center, make an arc with a radius of more than half of the measurement $\mathrm{EC}$. The arc intersects at point $\mathrm{H}$.

Step 9: Join the point $\mathrm{H}$ and $\mathrm{O}$, $\angle \mathrm{HOA}$ is the angle obtained of measurement $75°$.

Hence, $\angle \mathrm{HOA}$ is the required angle.