Please Help me it’s geometry

Question

asked May 26, 2021 90.0k views

1 Answer

Jwsample · Answer 1 · 2021-06-01T05:51:08+0000

Answer:

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.