Question

→
BD bisects ∠ABC
Find m∠ABD, m∠CBD, and m∠ABC

Answer 1

Answer:

As said in the question-

BD is a Bisector which is bisecting angle ABC, So it bisects it in 2 equal halves according to the property of bisector which states that a bisector divides the given figure in 2 EQUAL halves.

so,

angle ABD= angle CBD

> 8x+35°=11x+23°

35°-23°=11x-8x

12°=3x

12°/3= x

4°=x

putting x=4°

angle ABD=8x+35°=8×4+35°=32°+35°=67°

angle CBD=11x+23°=11×4+23°=44°+23°=67°

NOW,

angle ABC= angle ABD + angle CBD

= 67° + 67°

= 134°

ANSWER:

angle ABD= 67°

angle CBD= 67°

angle ABC= 134°

Answer 2

Given:

Bisector BD bisects ∠ABC.

∠ABD= (8x+35)°, ∠CBD= (11x+23)°.

To find:

m∠ABD, m∠CBD, and m∠ABC.

Solution:

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°.