BA=AD=DC with point D on segment BC. Angle ADC=135 degrees. What is the measure of angle ABC?
The figure shows two triangles next to each other. A is higher than B,D and C. Points BDC are all below A in that order from left to right.
- 1 decade agoBest Answer
BC is a straight line thus BDC is also
angle ADC=135 degrees thus angle ADB is 180-135 = 45degrees.
As BA = AD this is an iso triangle so angles ADB and ABC are the same.
Answer 45 degrees
- mohanrao dLv 71 decade ago
Draw the diagram
BAD and ADC are two isoscles triangles
in triangle ABD
BA = AD (given)
so angle ABD or ABC = angle ADB
angle ADC + angle ADB = 180(linear pair)
but angle ADC = 135 (given)
so 135 + angle ADB = 180
angle ADB = 180 -135 = 45
but angle ADB = angle ABC (proved)
so angle ABC = 45 degrees
ADB = ABC = 45 degrees
this is true even if AD is not equal to DC