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Examine the diagram, where quadrilateral LMNO is inscribed in O C.
M
L
C
82
N
O
© 2016 StrongMind. Created using GeoGebra.
If mZMNO = 82°, what is mZOLM?
O 102°
O 196°
O 98°
O 124

Examine the diagram where quadrilateral LMNO is inscribed in O C M L C 82 N O 2016 StrongMind Created using GeoGebra If mZMNO 82 what is mZOLM O 102 O 196 O 98 class=

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sqdancefan

Answer:

  (c)  98°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

  ∠OLM = 180° -∠ONM = 180° -82°

  ∠OLM = 98°

_____

Additional comment

The relation we used here derives from the fact that an inscribed angle is half the measure of the arc it intercepts. For two opposite angles of an inscribed quadrilateral, the sum of the arcs is 360°, so the sum of the angles will be 360°/2 = 180°.

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