Question

Lie on a strought

Answer 1

just a quick addition to the great work by Hrish ii above.

Check the picture below.

bearing in mind that twin sides stemming out of a vertex, BD and CD, make twin angles.

Answer 2

Answer:

25°

Step-by-step explanation:

In $\triangle BCD$

BD = CD .....(Given)

$\implies m\angle CBD = m\angle BCD$

(By isosceles triangle theorem)

$m\angle BCD = 60\degree....(given)$

$\implies m\angle CBD = 60\degree$

Now,

$m\angle CBD + m\angle ABD= 180\degree$

(Angles in linear pair)

$\implies 60\degree + m\angle ABD= 180\degree$

$\implies m\angle ABD= 180\degree - 60\degree$

$\implies m\angle ABD= 120\degree$

Next, in $\triangle ABD$

$m\angle BAD + m\angle ABD+ m\angle ADB= 180\degree$

(By interior angle sum postulate of a triangle)

$\implies 35\degree + 120\degree+ x= 180\degree$

$\implies 155\degree+ x= 180\degree$

$\implies x= 180\degree-155\degree$

$\implies x= 25\degree$