Question

ABCD Is a rhombus find m< ABC

Answer 1

If ABCD is a rhombus, then diagonals are perpendicular.

Therefore
`12y^o=90^o\to y^o=(90^o)/(12^o)=7.5^o`

`m\angle FCB=(4y-2)^o`

Substitute:

`m\angle FCB=(4(7.5)-2)^o=(30-2)^o=28^o`

We know: The sum of the measures of angles in a triangle is equal 180°.

Therefore we have the equation:

`m\angle FBC+28^o+90^o=180^o\\\\m\angle FBC+118^o=180^o\qquad\text{subtract}\ 118^o\ \text{from both sides}\\\\m\angle FBC=62^o`

BD is bisector of ∠ABC. Therefore
`m\angle ABF=m\angle FBC=62^o`

`m\angle ABC=m\angle ABF+m\angle FBC\\\\m\angle ABC=62^o+62^o=124^o`