Question

Construct an angle with the indicated measure.

$45°$.

Short answer

$\angle AOH=45°.$

Step-by-step solution

Step 1. Given information.   

An angle $45°$.

Step 2. Concept used.

Draw by using compass.

Step 3. Construction.

Step 1: Take any ray $\mathrm{O}{\rm A}$.

Step 2: With $\mathrm{O}$as centre and any radius, draw an arc cutting $\mathrm{O}{\rm A}$at$B$.

Step 3: With $B$as centre and the same radius, draw an arc cutting the first arc at$C$.

Step 4: With $C$as centre and the same radius, draw an arc cutting the first arc again at$D$

Step 5: With $C$and $D$as centre and radius of more than half of $CD$, draw two arcs cutting each other at${\rm E}$.

Step 6: Join$\mathrm{O}{\rm E}$.

Step 7: With $B$and ${\rm E}$ as centers, draw two arcs cutting each other at $F$ and join $OF$ such that $OF$ intersects the arc at $G$.

$\angle AOH=45°.$