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Question

Use the given figure to find the numerical value of angle x in degrees.
187794_f5ab7164cb8141d4bae01e85b87e5a4e.png

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Solution

Let the given triangle be ABC such that ABC=36. A line through C meets AB at D.
Now, In DBC,
DB=DC (Given)
hence, DBC=DCB=36 (Isosceles triangle property)
Sum of angles of triangle = 180
DBC+DCB+CDB=180
36+36+CDB=180
CDB=108
Now, ADC=180ADB
ADC=180108
ADC=72
in ADC,
ADC=DAC=72 (Isosceles triangle property, AC= CD is given)
Sum of angles = 180
ADC+CAD+ACD=180
72+72+x=180
x=180144
x=36

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