Question

Suppose point D is in the interior of ∠ABC

, m∠ABC=12x−110
, m∠ABD=3x+40
, and m∠DBC=2x−10
. W

Answer 1

`ABC = 130`

Explanation:

Given

`ABC=12x - 110`

`ABD=3x+40`

`DBC=2x - 10`

Required

Determine the measure of ABC --- Missing part of the question

First, we need to determine the value of x

Since, D is an interior of ABC, then

`ABC = ABD + DBC`

`12x - 110 = 3x + 40 + 2x - 10`

Collect Like Terms

`12x - 3x - 2x = 110 + 40 - 10`

`7x = 140`

Solve for x

`x = 140/7`

`x = 20`

Substitute 20 for x in
`ABC=12x - 110`

`ABC = 12 * 20 - 110`

`ABC = 240 - 110`

`ABC = 130`