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Mathematics

1 answer:

vovikov84 [41]3 years ago

6 0

9514 1404 393

Answer:

71°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

∠H = 180° -109° = 71°

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<em>Additional comment</em>

The above rule comes from the more general rule that the measure of an inscribed angle is half the measure of the arc it intercepts. Here, inscribed angle J intercepts arc GHI, so that arc has measure 2×109°. Then the measure of short arc GI is 360° -2×109°, and inscribed angle H is half that:

∠H = (1/2)(360° -2×109°)

∠H = 180° -109° = 71°

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