Question

in the figure find the value of x if a is bisector of angle A in triangle abc

Answer 1

Here,
In triangle ABC
angleA+B+C=180 (Interior angle of triangle)
50+30+angleA=180
80+A=180
A=180-80
A=100
therefore angleBAE=angleEAC=50 (AEbisectA)
In triangle AEC
angleA+E+C=180
50+E+30=180
angleE=100
now,
angleAEC+AED=180 (linear pair)
100+AED=180
AED=80
now,
angleABD+ADB+BAD=180
50+50+ADB=180
ADB=80

NOW angleADB+ADE=180
80+ADE=180
ADE=100
NOW IN triangleADE
angleA+D+E=180
x+100+80=180
x=0