Question

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

Answer 1

Let the given triangle be ABC such that $\angle ABC=36$. A line through C meets AB at D.
Now, In $△DBC$,
$DB=DC$ (Given)
hence, $\angle DBC=\angle DCB={36}^{\circ }$ (Isosceles triangle property)
Sum of angles of triangle = 180
$\angle DBC+\angle DCB+\angle CDB=180$
$36+36+\angle CDB=180$
$\angle CDB=108$
Now, $\angle ADC=180-\angle ADB$
$\angle ADC=180-108$
$\angle ADC={72}^{\circ }$
in $△ADC$,
$\angle ADC=\angle DAC={72}^{\circ }$ (Isosceles triangle property, AC= CD is given)
Sum of angles = 180
$\angle ADC+\angle CAD+\angle ACD=180$
$72+72+x=180$
$x=180-144$
$x={36}^{\circ }$