Question

Rhombus EfGH is shown in the diagram the measure of angle HEF =64 degrees. What is the measure of angle JGH.

Answer 1

In a rhombus opposite internal angles are congruent. This means that

`\measuredangle HEF=\measuredangle HGF=54`

Since diagonals bisect the angles of a rhombus, we have

`\measuredangle JGH=(\measuredangle HGF)/(2)`

Therefore, the answer is

`\begin{gathered} \measuredangle JGH=(54)/(2) \\ \measuredangle JGH=27 \end{gathered}`

that is, angle JGH measure 27 degrees.