Question

Examine the diagram, where quadrilateral LMNO is inscribed in O C.

M
L
C
82
N
O
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If mZMNO = 82°, what is mZOLM?
O 102°
O 196°
O 98°
O 124

Answer 1

(c) 98°

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°.