Answer:
C=98°
Step-by-step explanation:
Given:
[tex]m\angle EBC= 130\°[/tex]
Property of Rhombus to be used:
Opposite angles are congruent and diagonals bisect the angles at the corners.
[tex]\therefore m\angle EBC=m\angle EDC =130\°[/tex]
and [tex]m\angle BED=m\angle DCB[/tex]
We know that angle sum of all 4 interior angles =360°
[tex]\therefore m\angle EBC+m\angle EDC+m\angle BED+m\angle DCB=360\°[/tex]
[tex]\therefore m\angle BCD=m\angle BED=\frac{360-(130+130)}{2}=\frac{360-260}{2}=\frac{100}{2}=50\°[/tex]
[tex]m\angle BCE=\frac{\angle BCD}{2}[/tex] [As diagonal bisect the angles at the corners]
[tex]m\angle BCE=\frac{50}{2}[/tex]
∴ [tex]m\angle BCE=25\°[/tex]
[tex]m\angle BCE= C-73\°[/tex]
We solve for [tex]C[/tex]
Plugging [tex]m\angle BCE=25\°[/tex] and dding [tex]73\°[/tex] to both sides
[tex]25+73= C-73+73[/tex]
[tex]98= C[/tex]
[tex]\therefore C=98\°[/tex]
