Question

Construct angle of 112 degrees divide it in four ewual angles with compass protractor. Give diagram pic and steps how you make it? ​

Answer 1

Step-by-step explanation:

Steps of construction:

Step I- With the help of protractor, draw ∠80

∘

.

Step II - cut OA and OB at Q and P, taking P as the center and any convenient radius.

Step II - With vertex P, by using compass take more than half of arc PQ and draw arc.

Step III - With vertex Q , by using compass with same length, cut the previous arc at R.

Step IV- With help of ruler join the point O and R.

∴ ∠AOR = ∠ROB

Step V - similarly, bisect the arcs QS and SP

∴ ∠AOV = ∠VOR And ∠ROU = ∠UOB

Thus, ∠AOV, ∠VOR, ∠ROU and ∠UOB divide ∠BOA

in four equal parts

∴ ∠AOV = ∠VOR = ∠ROU = ∠UOB = 20

∘

Answer 2

Given:

An angle ABC = 112° is given.

Required:

To divide angle ABC into four equal angles with the help of compass.

Steps of construction:

1. Draw an angle ABC = 112° with the help of protractor.
2. With B as center, draw an arc of suitable radius to cut BA and BC at K and L respectively.
3. With center L draw an arc with radius more than half of LK.
4. With center K and without changing the radius draw an arc to cut the former arc at D.
5. Draw BD, which cuts the arc KL at M.
6. With L and M as centers draw arcs of suitable radius to cut each other at F.
7. With M and K as centers draw arcs of suitable radius to cut each other at E.
8. Draw BF and BE.

Answer:

Angle ABC =112° is dividend into four equal parts i.e Angle ABE, Angle EBD, Angle DBF and Angle FBC.