Answer:
Since there is an angle bisector, the two smaller angles are congruent, so we can set them equal to each other
∠ABD=∠CBD
We know ∠ABD is 3x+6, and ∠CBD is 7x-18, so we can substitute them in
Solve for x by getting x by itself
3x+6=7x-18
Subtract 3x from both sides
6=4x-18
Add 18 to both sides
24=4x
Divide both sides by 4
x=6
∠ABD
∠ABD=3x+6
We know x is 6, so we can substitute it in
∠ABD=3(6)+6
∠ABD=18+6
<u>∠ABD=24 </u>
∠CBD
∠CBD=7x-18
We know x is 6, so we can substitute it in
∠CBD=7(6)-18
∠CBD=42-18
<u>∠CBD=24</u>
∠ABC
∠ABC=∠CBD+∠ABD
We know ∠CBD and ∠ABD are both 24, so we can substitute them in
∠ABC=24+24
<u>∠ABC=48</u>
