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PQRSTUVW is a regular octagon, then the measure of $∠ V P Q$ is

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$22.5 °$

$112.5 °$

$37.5 °$

$135 °$

answer is C.

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Detailed Solution

Sum of interior angles of a regular octagon

$= (n - 2) 180 °$

$= (8 - 2) 180 °$

$= 6 \times 180 °$

$= 1080 °$

$∴ each interior angle = \frac{1080 °}{8} = 135 °$

$In Δ V W P, ∠ W V P + ∠ V W P + ∠ W P V = 180 °$

$x ° + 135 ° + x ° = 180 °$

$2 x ° + 135 ° = 180 °$

$2 x ° = 180 ° - 135 ° = 45 °$

$x = \frac{45 °}{2} = 22.5 °$

$∴ ∠ V P Q = 135 ° - 22.5 ° = 112.5 °$

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