# 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.

### 2 Answers

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- 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

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