Question

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

Answer 1

3x+6=7x-18 (they bisect)

x=6

angle abd= 24

angle cbd=24

angle abc = 48

Answer 2

The measurements are ∠ABD = 24° ∠CBD = 24° and ∠ABC = 48°  

Given:

BD bisects angle ABC

∠ABD = (3x+6)°  and ∠CBD = (7x-18)°

To find:

Find measurements of  ∠ABD,  ∠CBD and  ∠ABC

Solution:

Given that BD bisects ∠ABC which means BD will divide ∠ABC into equal angles

Then ∠ABD = ∠CBD

⇒  (3x+6)° = (7x-18)°

⇒ 4x = 24°

⇒  x = 6°  

The value of x = 6°

∠ABD = (3x+6)° = 3(6)+6 = 24°

∠CBD = (7x-18)° = 7(6)-18 = 24°

∠ABC = ∠ABD + ∠CBD = 24°+24° = 48°  

The measurements are ∠ABD = 24° ∠CBD = 24° and ∠ABC = 48°  

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