Question

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

Answer 1

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
`C`

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

`25+73= C-73+73`

`98= C`

`\therefore C=98\°`