Question

In the given figure, o is the mid- point of
AB and angle BQO = angle APO . Then angle OAP = ? ?​

Answer 1

Answer:

angle OBQ

Step-by-step explanation:

we know that opposite angle are equal as angle BOQ = angle AOP

Also given, angle APO = angle BQO

SO third angle of triangles will be automatically equal.

Answer 2

∠OAP = ∠OBQ

GIVEN

O is the mid-point of AB

∠BQO = ∠APO

TO FIND

∠OAP

SOLUTION

We can simply solve the above problem as follows;

In ΔAOP and ΔOQB

AO = OB (O is the mid point of AB)

∠BQO = ∠APO (Given)

∠AOP = ∠QOP (Vertically opposite angles)

By ASA similarity criterion

ΔAOP ≈ ΔOQB

Therefore,

∠OAP = ∠OBQ (By CPCT)

Hence,

∠OAP = ∠OBQ

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