In the figure, BA = AD = DC and point D is on segment BC. The measure of angle ACD is 22.5 degrees. What is the measure of angle ABC?

Thanks! ^^

AnonymousConfusedGuy
Feb 24, 2018

#1**+1 **

If BA = AD then by the law of sin s AngleABC = Angle ADB

If AD = DC then Angle DAC = Angle DCA = 22.5

A triangle has 180 degrees in it so angle ADC = 180 - 2(22.5) = 135 degrees

Angle ADC + ADB = 180 degrees (a straight line)

ADB = 180 - ADC = 180 - 135 = 45 degrees

Now see the red above? ADB = ABC = 45 degrees

ElectricPavlov
Feb 24, 2018

#1**+1 **

Best Answer

If BA = AD then by the law of sin s AngleABC = Angle ADB

If AD = DC then Angle DAC = Angle DCA = 22.5

A triangle has 180 degrees in it so angle ADC = 180 - 2(22.5) = 135 degrees

Angle ADC + ADB = 180 degrees (a straight line)

ADB = 180 - ADC = 180 - 135 = 45 degrees

Now see the red above? ADB = ABC = 45 degrees

ElectricPavlov
Feb 24, 2018