three squares are joined at their corners and strung between
two vertical poles as shown. Find the value of x'.
(A) 36
(B) 30°
(C) 41°
(D) 520
Answers
If the three squares are joined at their corners and strung between two vertical poles as shown, then the value of x is 41°.
Step-by-step explanation:
Step 1:
Let’s consider ABCDEFGHI as a 9 sided regular polygon, so,
The sum of interior angles of a regular polygon is given by,
= (2n-4) * 90° …… [where n = no.of sides = 9]
= (2*18 – 4) * 90°
= 1260°
Step 2:
We are given in the figure,
∠AIH = 30°
∠HGF = 124°
∠FED = 75°
∠BCD = x
Now,
The measure of reflex angles are as follows:
∠IHG = ∠GFE = ∠EDC = 360° - 90° = 270° …… [since angles of the square, ∠IHG = ∠GFE = ∠EDC = 90°]
Step 3:
Therefore,
The sum of all the interior angles of the regular polygon ABCDEFGHI i.e.,
∠AIH + ∠HGF + ∠FED + ∠BCD + ∠IHG + ∠GFE + ∠EDC + ∠IAB + ∠CBA = 1260°
⇒ 30° + 124° + 75° + x + (3 * 270°) + 90° + 90° = 1260°
⇒ x + 1219° = 1260°
⇒ x = 1260° - 1219°
⇒ x = 41°
Thus, the value of x is option (C): 41° .
Hope this is helpful!!!!
Answer:
Step-by-step explanation:
If the three squares are joined at their corners and strung between two vertical poles as shown, then the value of x is 41°.
Step-by-step explanation:
Step 1:
Let’s consider ABCDEFGHI as a 9 sided regular polygon, so,
The sum of interior angles of a regular polygon is given by,
= (2n-4) * 90° …… [where n = no.of sides = 9]
= (2*18 – 4) * 90°
= 1260°
Step 2:
We are given in the figure,
∠AIH = 30°
∠HGF = 124°
∠FED = 75°
∠BCD = x
Now,
The measure of reflex angles are as follows:
∠IHG = ∠GFE = ∠EDC = 360° - 90° = 270° …… [since angles of the square, ∠IHG = ∠GFE = ∠EDC = 90°]
Step 3:
Therefore,
The sum of all the interior angles of the regular polygon ABCDEFGHI i.e.,
∠AIH + ∠HGF + ∠FED + ∠BCD + ∠IHG + ∠GFE + ∠EDC + ∠IAB + ∠CBA = 1260°
⇒ 30° + 124° + 75° + x + (3 * 270°) + 90° + 90° = 1260°
⇒ x + 1219° = 1260°
⇒ x = 1260° - 1219°
⇒ x = 41°
Thus, the value of x is option (C): 41° .