In Fig. 9.45, if AB ⊥ BC, then x =
A. 18
B. 22
C. 25
D. 32
Answers
Given : AB ⊥ BC
From figure :
∠BDE = x + 14°
AB is perpendicular to BC so, ∠B = 90°.
∠BEC = 32°
[Vertically opposite angles]
In ∆BDE,
We know that the sum of all three angles of a ∆ is 180°.
∠BDE + ∠BED + ∠DBE = 180°
∠BDE + (∠BEC + ∠CED) + ∠DBE = 180°
(x + 14°) + (32° + x) + 90° = 180°
2x + 136° = 180°
2x = 180° - 136°
2x = 44°
x = 44°/2
x = 22°
Hence the value of x is 22°.
Among the given options option (B) 22° is correct.
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Answer:
x is 22°
Step-by-step explanation:
Given : AB ⊥ BC
From figure :
∠BDE = x + 14°
AB is perpendicular to BC so, ∠B = 90°.
∠BEC = 32°
[Vertically opposite angles]
In ∆BDE,
We know that the sum of all three angles of a ∆ is 180°.
∠BDE + ∠BED + ∠DBE = 180°
∠BDE + (∠BEC + ∠CED) + ∠DBE = 180°
(x + 14°) + (32° + x) + 90° = 180°
2x + 136° = 180°
2x = 180° - 136°
2x = 44°
x = 44°/2
x = 22°
Hence the value of x is 22°.
Among the given options option (B) 22° is correct.