Question

Let, ∠ABC = 60°and CB be produced to the point D. Now, BX is a ray from B and the point X lies on that side of DC where A lies and ∠ABX ∶ ∠DBX = 5 ∶ 7. Draw the figure and then find (i) ∠CBX (ii) ∠DBX (iii) Reflex ∠ABX.​

Answer 1

Given : ∠ABC = 60°and CB be produced to the point D.

Now, BX is a ray from B and the point X lies on that side of DC where A lies and

∠ABX ∶ ∠DBX = 5 ∶ 7.

To find :  (i) ∠CBX (ii) ∠DBX (iii) Reflex ∠ABX.

Solution:

∠ABC = 60°

CB be produced to the point D.

=> ∠ABC and ∠ABD form a linear pair

=> 60°  +  ∠ABD = 180°

=>  ∠ABD = 120°

∠ABD = ∠ABX +∠DBX  = 120°

∠ABX ∶ ∠DBX = 5 ∶ 7.

=> ∠ABX  = 50°  ,   ∠DBX = 70°

∠CBX  = ∠ABC  +  ∠ABX  

=>  ∠CBX   = 60° + 50° = 110°

Reflex ∠ABX. = 360° - ∠ABX = 360° - 50°  = 310°

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