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Let us have a triangle ABC and a point D on BC such that BD=DC=DA. If angle ACB=50 then how many degrees are in angle ABC?

 Feb 26, 2021
 #1
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because CD=AD, triangle CAD is iscoscolese, so angle CAD is 50 as well, which makes CDA 80, and because D is on CB, angle ADB+ADC=180, so ADB=80, and because AD=BD, ADB is an iscoscolese triangle, so angle ABC=(180-80)/2=$\boxed{50^\circ}$

 Feb 26, 2021
 #2
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ΔABD is an isosceles triangle.

 

Angle ABD = 100 degrees, and angles ABD and BAD are congruent.

 

Angle ABC = 1/2(180 - 100) = 40 degrees

 Feb 26, 2021
edited by Guest  Feb 26, 2021

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