Question

9. If PORS is a rhombus, find mZPOR. (4x - 27) A (2x + 7) I R

Answer 1

Rhombus

Diagonals bisect the angles of a rhombus, that is, angle Q is bisected by the diagonal and the angles are equal, thus:

4x - 27 = 2x + 7

Subtracting 2x:

4x - 2x - 27 = 7

Adding 27:

4x - 2x = 7 + 27

Operating:

2x = 34

Dividing by 2:

x = 34/2

x = 17

Now we find the measure of angle PQR:

`\begin{gathered} m\angle PQR=4x-27+2x+7 \\ \text{Operating:} \\ m\angle PQR=6x-20 \end{gathered}`

Substituting x=17:

`m\angle PQR=6\cdot17-20=82`