Inscribed Quadrilateral Theorem Inscribed Quadrilateral Theorem: If quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Note: All
the vertices of the quadrilateral must lie on the circle.
Example 1: Find the indicated measures. Step 1: Determine if the all the vertices of the figure lie on the circle.
(2 +53)
No, not inscribed
R(15y + 17)
Yes, Inscribed
Step 2: Using the Inscribed Quadrilateral theorem, select a pair of opposite
angles and solve for the value y.
(5y + 3)
SPQ
LPQR
O LORS
O ZRSP
P
Step 3: Find the measure of each angle.
a. m SPQ=
b. mzPQR =
C. MZQRS =
d. mZRSP
Notes

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

c

step-by-step explanation:

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