Question

Ray BD bisects angle abc. Find the m angle abd m angle cbd and m abc

Answer 1

m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°;

Bisector BD bisects ∠ABC.

∠ABD= (8x+35)°, ∠CBD= (11x+23)°.

As given, bisector BD bisects the angle ABC so this means, the angle ABC is divided into two halves.

So,

angle ABD= angle CBD.

and ∠ABD= (8x + 35)° (i)

∠CBD= (11x + 23)° (ii)

So,

(8x + 35)° = (11x + 23)°

On solving the above equation, we have

3x= 12

x= 4.

Putting x=4 in (i) we have,

∠ABD= 8(4) + 35

∠ABD= 67°

As ∠ABD = ∠CBD, we have

∠CBD= 67°

Now,

∠ABC= ∠ABD + ∠CBD

∠ABC= 67° + 67°

∠ABC= 134°.

Hence, m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.

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