Given:
The figure of a rhombus QRST.
To find:
A. The value of x.
B. The measure of angle RQP.
Solution:
A. We need to find the value of x.
We know that the diagonals of a rhombus are perpendicular bisectors. It means the angles on the intersection of diagonals are right angles.
[tex]m\angle RPS=90^\circ[/tex] [Right angle]
[tex](5x+15)^\circ=90^\circ[/tex]
[tex](5x+15)=90[/tex]
[tex]5x=90-15[/tex]
[tex]5x=75[/tex]
Divide both sides by 5.
[tex]x=\dfrac{75}{5}[/tex]
[tex]x=15[/tex]
Therefore, the value of x is 15.
B. We need to find the measure of angle RQP.
From the given figure, it is clear that
[tex]m\angle RQP=(2x+3)^\circ[/tex]
Putting [tex]x=15[/tex], we get
[tex]m\angle RQP=(2(15)+3)^\circ[/tex]
[tex]m\angle RQP=(30+3)^\circ[/tex]
[tex]m\angle RQP=33^\circ[/tex]
Therefore, the measure of angle RQP is 33 degrees.
