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# Another short question

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+779

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
+12119
+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

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

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

ElectricPavlov  Feb 24, 2018
Sort:

#1
+12119
+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

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

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

ElectricPavlov  Feb 24, 2018
#2
+779
+1

Thank you so much!

AnonymousConfusedGuy  Feb 24, 2018

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