Construct the following angles using ruler and compass and verify by measuring them by a protractor.

75^o

Step of construction:

Step 1: Draw a ray OA.

Step 2: With its initial point O as center and any radius, draw an arc, cutting OA at C.

Step 3: With center c and same radius (as in step 2) draw an arc cutting arc at D.

Step 4: With D as center and the same radius, draw an arc cutting the arc cutting at E.

Step 5: With D and E as centers and any convenient radius (more than DE). Draw to two arcs intersecting at P.

Step 6: Join OP. Then ∠AOP = 90°

Step 7:Bisect ∠BOP so that ∠BOQ = ∠BOP

= (∠AOP - ∠AOB)

= (90° -60°) = × 30° = 15°

So, we obtain

∠AOQ = ∠AOB + ∠BOQ

= 60° + 15° = 75°

Verification:

On measuring ∠AOQ, with the protractor,

we find ∠ AOQ = 75° .