Question

How do you solve this and what are the properties you use to obtain x, please list all the properties

Answer 1

Answer:

hey your answer is as follows

so pls mark it as brainliest

refer the reference diagram uploaded above for better understanding

Step-by-step explanation:

so now here let the centre of adjoining circle be point O

so here angle bac=40 and it intercepts arc bc on circumference of circle

therefore by inscribed angle theorem

we get

angle bac=1/2×m(arc bc)

ie m(arc bc)=40×2=80 degree

so here angle boc is a central angle

so we know that measure of arc subtended ie intercepted by central angle on circumference of circle is of same measure as that of central angle

so hence angle boc=m(arc bc)=80 (1)

now here pb and pc are tangents as well as tangent segment drawn from external point P

so by tangent theorem

we get

angle b=angle c=90 degree (2)

so considering quadrilateral pboc

angle b+angle c+angle o+angle p=360

thus x+90+90+80=360 from (1) and (2)

ie x=360-(90+90+80)

=360-(180+80)

=360-260

=100 degrees

hence value of x ie measure of angle p is 100 degrees