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.

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  • 1 decade ago
    Best 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

  • 1 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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