Question

Pls Help!!
Find m/ABC if BD is an angle bisector.

Answer 1

`\large\boxed{\tt \angle ABC = 146^(\circ).}`

Explanation:

`\textsf{We are asked to solve for} \ \tt \angle ABC. \ \textsf{We are given that} \ \overrightarrow{\tt BD} \ \textsf{is an \underline{Angle Bisector}.}`

`\large\underline{\textsf{What are Angle Bisectors?}}`

`\textsf{Angle Bisectors are \underline{Line Segments} that bisect a full angle into 2 congruent angles.}`

`\textsf{Think of Angle Bisectors as cutting something into half, both pieces will be congruent.}`

`\large\underline{\textsf{Solving;}}`

`\textsf{Because} \ \overrightarrow{\tt BD} \ \textsf{is an Angle Bisector, then} \ \angle \tt ABD \cong \angle CBD. \ \textsf{This will mean that both}`

`\textsf{angles are \underline{congruent} to each other, hence their measures are the same.}`

`\tt 4a+13=7a-32`

`\textsf{Let's begin solving for a, afterwards we should substitute a back into} \ \tt \angle ABD, \ \textsf{multiply}`

`\textsf{the angles' measure by 2 since} \ \tt \angle CBD \cong \angle ABD, \ \textsf{then we are able to identify the}`

`\textsf{measure of} \ \tt \angle ABC.`

`\underline{\textsf{Find the value of a;}}`

`\tt 4a+13=7a-32`

`\underline{\textsf{Subtract 7a from both sides of the equation;}}`

`\tt 4a-7a+13=7a-7a-32`

`\tt -3a+13=-32`

`\underline{\textsf{Subtract 13 from both sides of the equation;}}`

`\tt -3a+13-13=-32-13`

`\tt -3a=-45`

`\underline{\textsf{Divide both sides of the equation by -3;}}`

`\large\boxed{\tt a=15}`

`\underline{\textsf{Substitute 15 back into} \ \tt \angle ABD;}`

`\tt \angle ABD = 4(15) + 13`

`\tt \angle ABD = 73^(\circ)`

`\underline{\textsf{Multiply} \ \tt \angle ABD \ \textsf{by 2;}}`

`\tt \angle ABD \ + \ \angle CBD= 73^(\circ) * 2`

`\tt \angle ABD \ + \ \angle CBD= 146^(\circ)`

`\textsf{146}^(\circ) \ \textsf{represents the value of} \ \tt \angle ABC.`

`\large\underline{\textsf{Hence;}}`

`\large\boxed{\tt \angle ABC = 146^(\circ).}`