Answer:
25°
Step-by-step explanation:
In [tex]\triangle BCD[/tex]
BD = CD .....(Given)
[tex]\implies m\angle CBD = m\angle BCD[/tex]
(By isosceles triangle theorem)
[tex]m\angle BCD = 60\degree....(given)[/tex]
[tex]\implies m\angle CBD = 60\degree[/tex]
Now,
[tex]m\angle CBD + m\angle ABD= 180\degree[/tex]
(Angles in linear pair)
[tex]\implies 60\degree + m\angle ABD= 180\degree[/tex]
[tex]\implies m\angle ABD= 180\degree - 60\degree[/tex]
[tex]\implies m\angle ABD= 120\degree[/tex]
Next, in [tex]\triangle ABD[/tex]
[tex]m\angle BAD + m\angle ABD+ m\angle ADB= 180\degree[/tex]
(By interior angle sum postulate of a triangle)
[tex]\implies 35\degree + 120\degree+ x= 180\degree[/tex]
[tex]\implies 155\degree+ x= 180\degree[/tex]
[tex]\implies x= 180\degree-155\degree[/tex]
[tex]\implies x= 25\degree[/tex]
