Find the angle measurement

Question

I'm in geometry and this is a problem I've been stuck on for a while now, "there exists a point T on the interior of <(angle sign)ABC such that BT->(ray sign) is an angle bisector. m<ABC=3x-5 and m<ABT=x+10. Find the m<ABC."

Answer 1

<ABC such that BT is an angle bisector

Angle bisector divides angle into two equal angles

 

so

 

2 m<ABT = m<ABC

 

2(x+10) =3x -5

 

2x + 20 = 3x -5

 

20 =x -5

 

x =25

 

so < ABC =3x- 5 =3(25)-5= 75 -5 =70