Quadrilateral BCDE is a rhombus and mZBCE = C - 73°. What is the value of c?

Question

asked Sep 5, 2020 99.8k views

1 Answer

Manuel Lopera · Answer 1 · 2020-09-11T21:47:14+0000

Answer:

C=98°

Explanation:

Given:

$m\angle EBC= 130\°$

Property of Rhombus to be used:

Opposite angles are congruent and diagonals bisect the angles at the corners.

$\therefore m\angle EBC=m\angle EDC =130\°$

and
$m\angle BED=m\angle DCB$

We know that angle sum of all 4 interior angles =360°

$\therefore m\angle EBC+m\angle EDC+m\angle BED+m\angle DCB=360\°$

$\therefore m\angle BCD=m\angle BED=(360-(130+130))/(2)=(360-260)/(2)=(100)/(2)=50\°$

$m\angle BCE=(\angle BCD)/(2)$ [As diagonal bisect the angles at the corners]

$m\angle BCE=(50)/(2)$

∴
$m\angle BCE=25\°$

$m\angle BCE= C-73\°$

We solve for

Plugging
$m\angle BCE=25\°$ and dding
$73\°$ to both sides

25+73= C-73+73

98= C

$\therefore C=98\°$