Question

Construct an angle of 45o at the point of origin of a given ray and write the step of construction.

Answer 1

Step-by-step explanation:

Draw a ray OY.

Then, take O as the centre and any radius, mark a point A on the arc ABC.

Step 2: Now, taking A as the centre and the same radius, mark a point B on the arc ABC.

Step 3: Take B as a centre and the same radius, mark a point C on the arc ABC.

step 3

Step 4: Now, taking C and B as centre one by one, draw an arc from each centre intersecting each other at a point X.

step 4

Step 5: X and O are joined and a ray making an angle 90^{\circ} with OY is formed.

Let the arc AC touches OX at E

Step 6: With A and E as centres, 2 arcs are marked intersecting each other at D and the bisector of angle XOY is drawn.

step 5

Justification:

By construction we have,

\angle XOY = 90^{\circ}

We constructed the bisector of \angle XOY as \angle DOY

Thus,

\angle DOY = \frac{1}{2}\angle XOY = \frac{1}{2}\times90^{\circ} = 45^{\circ}