Question

find the value of x in given figure ( c=40)​

Answer 1

Answer:

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so here we go

Step-by-step explanation:

now here angle c=40

also here ob and oa are radii of adjoining circle

so thus ao=bo (radii of same circle)

so as in triangle boa two sides except it's base are equal

triangle boa is an isoceles triangle

so hence angle oba=angle oab=x

because of isoceles triangle theorem (1)

now angle c intercepts arc ab on circumference of circle

so by inscribed angle theorem

we get m(arc ab)=80

as the arc intercepted by the angle on its circumference is twice than the angle subtended by that arc

so now arc ab angle boa would be equal

because as angle boa is an central angle the arc intercepted by it on its opposite side are equal

hence angle boa=80

thus apply angle sum property on triangle boa

you get angle boa+x+x=180 (from 1)

so 80+2x=180

so 2x=100

hence x=50

thus angle boa and oab are each of 50 degree measure