Question

Construct the following angles and verify by measuring them by a protractor:
${135}^o$

Answer 1

${60}^{\circ }+{60}^{\circ }={120}^{\circ }$

${120}^{\circ }+\frac{{60}^{\circ }}{2}={120}^{\circ }+{30}^{\circ }$

$={120}^{\circ }+\frac{{30}^{\circ }}{2}$

$={120}^{\circ }+{15}^{\circ }$

$={135}^{\circ }$

Step 1: A ray $OA$ is drawn.

Step 2: An arc $OB$ is drawn with $O$ as a centre.

Step 3:With the same length $BC$ and from $C$ which touches the base line.

Step 4: Construct a perpendicular bisector to another arc which is $C$ to the base line.Join $OE$

Step 4: Construct a perpendicular bisector to another arc which is $CE$ .Join $OD$

$\therefore \angle AOC={90}^{\circ }$

Step 5: Construct a perpendicular bisector from $C$ to another point of the arc .Join $OD$

$\therefore \angle AOD={135}^{\circ }$

Thus,$\angle AOD$ is the required angle making ${135}^{\circ }$