CK-12 Geometry-Concepts

9.6. Inscribed Quadrilaterals in Circles http://www.ck12.org

Example B

Find the value of the missing variable.

It is easiest to figure outzfirst. It is supplementary with 93◦, soz= 87 ◦. Second, we can findx.xis an inscribed angle
that intercepts the arc 58◦+ 106 ◦= 164 ◦. Therefore, by the Inscribed Angle Theorem,x= 82 ◦.yis supplementary
withx, soy= 98 ◦.Find the value of the missing variables.

Example C

Findxandyin the picture below.

The opposite angles are supplementary. Set up an equation forxandy.

( 7 x+ 1 )◦+ 105 ◦= 180 ◦ ( 4 y+ 14 )◦+( 7 y+ 1 )◦= 180 ◦

7 x+ 106 ◦= 180 ◦ 11 y+ 15 ◦= 180 ◦

7 x= 84 ◦ 11 y= 165 ◦

x= 12 ◦ y= 15 ◦

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52421

CK-12 Foundation: Chapter9InscribedQuadrilateralsinCirclesB