Question

Find the measures of the numbered angles in the kite shown below.

Answer 1

The given quadilateral is a kite.

The diagonal of the kite intersect perpendicularly.

The value of angle 2 can be determined as,

$\begin{gathered} \angle2=90^{\circ}-27^{\circ} \\ =63^{\circ} \end{gathered}$

The value of angle 3 can be determine as,

$\angle3=\angle2=63^{\circ}$

In triangle PQR,

$\begin{gathered} \angle PQO=\angle RQO \\ =27^{\circ} \end{gathered}$

In triangle PSR,

$\angle1=\angle SRO$

In triangle SPO,

$\angle PSO=90^{\circ}-\angle1$

Also in triangle PSR,

$\angle PSO=\angle RSO=90^{\circ}-\angle1$

The value of angle 1 can not be determined without any further data.