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.