Question

In the given figure CBA is a tangent to the circle centered at O and DOB is a straight line If PQ is parallel to the CBA and angle PBC =69° then measure of angle QBA is equal to

Answer 1

Answer:

ANGLE QBA= 69'

Step-by-step explanation:

Angle PBC = 69'  GIVEN

Angle, PQB = PBC = 69'       Angle In Alternate Segment  

CBA is parrallel to PQ, Hence Angle, PQB = QBA = 69'

Therefore, ANGLE QBA = 69' ....................................

Answer 2

We know that the point of contact of circle is 90 degrees

obc=90.....(1)

pbc=69.....(2)

And, obp=obc-pbc

obp=90-69(from (1) & (2))

obp=21 degrees..... (3)

Since, ob is perpendicular bisector

It bisects the angle qbp into two equal parts (I. E obq=obp)

So, obq = 21 degrees......(4)

AC is a line (I.E=180)

pbc+obq+obp+qba=180(linear pair)

From (2),(3)&(4)we have,

69+21+21+qba=180

qba=69 degrees

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