Question

In the figure shown, suppose m∠ABC = n and m∠ABD = 2(m∠DBC). The angle bisector of ∠DBC is ⟶BE. What is m∠EBC

Answer 1

Answer: n/6

Step-by-step explanation:

if ABD= 2*DBC, then ABD= 4*EBC, since EBC is half of DBC. So, n= ABD+DBC. To find EBC it would be n=4EBC(value of ABD)+2EBC(value of DBC). That gives you n=6EBC, divide 6 from both sides, which gives you your answer.

Answer 2

Given:   m∠ABC = n and m∠ABD = 2(m∠DBC).

The angle bisector of ∠DBC is  BE.

To Find :  m∠EBC

Solution:

m∠ABC = m∠ABD + m∠DBC

m∠ABD = 2(m∠DBC) given

=> m∠ABC = 2(m∠DBC) + m∠DBC

=> m∠ABC = 3(m∠DBC)   ...Eq1

The angle bisector of ∠DBC is  BE.

=> m∠EBC = (1/2) (m∠DBC)

=> 2m∠EBC = m∠DBC

Substitute  m∠DBC = 2(m∠EBC)  in  Eq1

=> m∠ABC = 3( 2(m∠EBC))

=>  m∠ABC = 6(m∠EBC)

Given m∠ABC = n

=> n = 6(m∠EBC)

=> n/6 = m∠EBC

Hence m∠EBC is n/6

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