Question

Geometry Bisects Help

Answer 1

m∠ABC = 72

Explanation:

`\text{If}\ \overrightarrow{BD}\ \text{bisects}\ \angle ABC,\ \text{then}\ \angle ABD\cong\angle DBC\to m\abgle ABD=m\angle DBC.\\\\\text{We have}\ m\angle ABD=12x+24\ \text{and}\ m\angle DBC=20x+16.\\\\\text{Make the equation:}\\\\12x+24=20x+16\qquad\text{subtract 24 from both sides}\\\\12x=20x-8\qquad\text{subtract}\ 20x\ \text{from both sides}\\\\-8x=-8\qquad\text{divide both sides by (-8)}\\\\x=1\\\\m\angle ABC=m\angle ABD+m\angle DBC=2m\angle ABD`

`m\angle ABD=12x+24\\\\\text{Put}\ x=1\ \text{to the equation:}\\\\m\angle ABD=12(1)+24=12+24=36\\\\m\angle ABC=(2)(36)=72`