Question

Please Help me it’s geometry

Answer 1

Option C.

Explanation:

Given: In
`\Delta OPQ,m\angle O=107^(\circ),m\angle P=28^(\circ)`.

In
`\Delta OPQ`,

`m\angle O+m\angle P+m\angle Q=180^(\circ)` (Angle sum property)

`107^(\circ)+28^(\circ)+m\angle Q=180^(\circ)`

`135^(\circ)+m\angle Q=180^(\circ)`

`m\angle Q=180^(\circ)-135^(\circ)`

`m\angle Q=45^(\circ)`

Now,

`m\angle O>m\angle Q>m\angle P`

In a triangle, the greatest angle has largest opposite side and smallest angle has smallest opposite side. So, we conclude that

`PQ>OP>QO`

Therefore, the correct option is C.