Question

50 points please HELP! show work aswell THANK YOU!!!

Answer 1

m∠DBC = 70°

Explanation:

When an angle is bisected, it is divided into two equal parts.

Therefore, if BD bisects ∠ABC, then m∠ABD = m∠DBC.

Since ∠ABC is the sum of ∠ABD and ∠DBC, then:

`m\angle ABC=m\angle ABD + m\angle DBC`

`m\angle ABC=m\angle DBC + m\angle DBC`

`m\angle ABC=2 \cdot m\angle DBC`

Given that m∠ABC = 140°, then:

`140^(\circ)=2 \cdot m\angle DBC`

So this means that m∠DBC must be half of 140°:

`m\angle DBC =(140^(\circ))/(2)=70^(\circ)`