Question

Please Help me it’s geometry

Answer 1

Answer:

Option C.

Step-by-step 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.