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Question
If two set squares, one of 45⁰-90⁰-45⁰ and other of 30⁰-60⁰-90⁰, are placed alongside as shown in the figure below, find the angle between the set squares.
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Solution
We have two set squares viz., set square ABC which is of 45⁰-90⁰-45⁰ and set square CDE of 30⁰-60⁰-90⁰ placed alongside each other.
Now we can see that:
∠ACB = 45⁰ and ∠ECD = 60⁰
Also, both the set squares are placed on the straight line.
Therfore by the property of linear pair of angles:
∠ACB + ∠ACD + ∠DCE = 180⁰
=> 45⁰ + ∠ACD + 60⁰ = 180⁰
=> ∠ACD = 180⁰ - 105⁰
=> ∠ACD = 75⁰.
Hence the angle between the set squares placed as shown is equal to 75⁰.
Now we can see that:∠ACB = 45⁰ and ∠ECD = 60⁰
Also, both the set squares are placed on the straight line.
Therfore by the property of linear pair of angles:
∠ACB + ∠ACD + ∠DCE = 180⁰
=> 45⁰ + ∠ACD + 60⁰ = 180⁰
=> ∠ACD = 180⁰ - 105⁰
=> ∠ACD = 75⁰.
Hence the angle between the set squares placed as shown is equal to 75⁰.
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