+159 Segment AD bisects angle BAC. If BD=DA=AC, what is angle AC in degrees?
+129852 Don't know what angle "AC" is...but if you want to know the angles, we have
Because BD = AD.....then angle ABD = angle BAD.....let these angle measures = x
And because AC = AD....then angle ADC = angle ACD.....let these angle measures = y
In triangle ABD, using the Exterior Angle Theorem, angle ADB = x + y
In triangle DAC, angle DAC = angle BAD = x
So....we have the following system.....
x + x + x + y = 180 ⇒ 3x + y = 180 ⇒ -6x - 2y = -360 (1)
x + 2y = 180 (2)
Add (1) and (2) and we get that
-5x = -180
x = 36°
And using (2)
36 + 2y = 180
2y = 144
y = 72°
So angles ABD, ADB, DAC = 36°
And angles ADC, ACD = 72°
And angle ADB = 36 + 72 = 108°
