Question

In the adjoining figure ,two circles intersect at points P and Q. If angle A = 80° and angle D = 84°, calculate (i) angle QBC (ii) angle BPC

Answer 1

we know that a quadrilateral opp angles are supplementary so

angle DAB+ANGLE DCB=180 °

NOW ,

ANGLE DCB=180°-50°=40°

NOW ,

ANGLE ADB+ANGLE ABC=180°

SO,ANGLE ABC=180°-84°=96°

HOPE IT HELPS

Answer 2

Answer:

Step-by-step explanation:

Opposite angles of a cyclic quadrilateral are supplementary.

Draw seg PQ.

Now,

Angle ADP + angle PQA=180°

AnglePQA= 180°-84°

96°

Now

Angle CBQ and Angle PQA are congruent as they are corresponding angles.

Hence,

Angle CBQ=96°

Now angle BPC= 1/2 of angle CBQ

By cyclic quadrilateral theroem,

Angle QPC = 84°

Hence angle BPC= 84× 1/2

= 42°