Question

In

△
O
P
Q
,
△OPQ,
O
P
‾
≅
Q
O
‾
OP
≅
QO
​
and
m
∠
Q
=
4
8
∘
.
m∠Q=48
∘
. Find
m
∠
O

Answer 1

∠O = 84°

Explanation:

In ΔOPQ,

OP ≅ OQ

So, ΔOPQ is an isosceles triangle.

∠P = ∠Q {Angels opposite to equal sides are equal}

∠P = 48°

In ΔOPQ,

∠P + ∠Q + ∠O = 180° {Angle sum property of triangle}

48 + 48 + ∠O = 180

96 + ∠O = 180

∠O = 180 - 96

∠O = 84°