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Sagot :
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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