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

Find the measures of the numbered angles in the kite shown below.-example-1

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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.

Find the measures of the numbered angles in the kite shown below.-example-1
User Eden Sharvit
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