This question was uploaded on my Instagram, Facebook and Twitter account on 17th of August 2021. You can check it on my Social media account. Kindly follow my accounts for daily new puzzles. You will get daily one puzzle at 4.00 UTC (Convert it as per your country timing).
One square is placed on another square at 45°. Length of line joining first vertices of large square and farthest vertices of small square is same as diagonal of large square. Find angle between side of square and line joining first vertices of large square and nearest vertices of small square.
Give this question a try then check your answer with solution.
(Shortcut Image Solution with Calculations is gives below in this post)
Step 1:
Give names to all vertices.
Join bottom of diagonal of large square with left and right vertices of small square.
Join left and right vertices of small square.
Step 2:
In △ACE,
All sides are same.
⇒ △ACE is equilateral triangle.
In △CDG and △CDE,
CD is common side,
Angles at D for both triangle are same (135°)
GD = ED ----- (Sides of square)
⇒ △CDG ≅ △CDE
⇒ CG = CE and ∠DCG = ∠DCE = 15°
⇒ ∠ECG = 30° = ∠ACG
Step 3:
In △ECG and △ACG,
AC = GC = EC
Angles at C for both triangle are same (30°)
⇒ △CDG ≅ △CDE
⇒ AG = GE
Step 4:
At ∠GEC,
∠ACE = 60°
⇒ ∠AED = ∠CED = 30°
⇒ ∠GEA = 45 - 30 = 15°
In △AGE,
AG = GE
⇒ ∠GEA = ∠GAE = 15°
⇒ ∠AGE = 150°
Step 5:
α = 150 - 45 = 105°
Image Solution:
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