Question

Construct an angle of 90° at the initial point of a given
construction.
Construct an angle of 45° at the initial point of a given
construction.
Construct the angles of the following measurements:
(i) 30°
1°
(ii) 22
2
1 22
(iii) 15
Construct the following angles and verify by measuring them b
(i) 75°
(ii) 105°
(iii) 13
Construct an equilateral triangle, given its side and justify the​

Answer 1

Answer:

a. 30° is the correct answer

B. 75° is the correct answer

Step-by-step explanation:

Steps of construction

a. Take a ray with initial point A.

Taking care center and same radius draw an Arc of a circle which intersect AB at C.

With C as Centre and the same radius, draw an arc intersecting the previous arc at E.

With E as Centre and the same radius draw an arc which intersects the arc drawn in step 2 at F.

With E as Centre and the same radius, draw another arc, intersecting the previous arc at G.

Draw the ray AG.

Then ∠BAG is the required angle 90°

Justification:

Join AE, CE, EF and AE, AF

AC = CE = AE [ by construction]

∴ ACE is an equilateral Triangle

⇒ ∠CAE = 60° —————–1

Similarly, AE = EF = AF

∴Triangle AEF is an equilateral Triangle

⇒ ∠EAF = 60°

Because AG bisects ⇒ ∠EAF

∴∠GAE = 1\2 = 30° = 30°————2

1+2

∴∠CAE + ∠GAE = 60°+30°

∠GAB=30°

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B. don't know know explanation

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