MCQ
In the given figure, chords $AB$ and $CD$ intersect at $P.$ If $\angle\text{DPB}=88^\circ$ and $\angle\text{DAP}=46^\circ,$ then the measure of $\angle\text{ABC}$ is:
- A$44^\circ $
- ✓$42^\circ$
- C$48^\circ$
- D$46^\circ$
✓
Answer
Correct option: B.
$42^\circ$
$\angle\text{PCB}=46^\circ ($Angles of same arc$)$
$\angle\text{CPB}=180^\circ-88^\circ=92^\circ ($Linear Pair$)$
So, $\angle\text{PBC}=180^\circ-46^\circ-92^\circ=42^\circ ($Using angle sum property in triangle $PCB)$
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