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Solve for a and b in the following circles:
A)

Solve for a and b in the following circles: A)-example-1
User Thenosic
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1 Answer

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Given:

A quadrilateral inscribed in a circle.

To find:

The values of a and b.

Solution:

A quadrilateral inscribed in a circle. So, the quadrilateral is a cyclic quadrilateral.

We know that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees.


a+79^\circ=180^\circ


a=180^\circ-79^\circ


a=101^\circ

We know that the measure of arc is twice of measure of subtended angle on that arc.


(110^\circ+b)=2(96^\circ)


110^\circ+b=192^\circ


b=192^\circ-110^\circ


b=82^\circ

Therefore, the value of a is 101 degrees and the value of b is 82 degrees.

User Ynkr
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