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Measuring Angles

The measures ...

Question

The measures of $∠ a, ∠ b, ∠ c, ∠ d, ∠ e, a r e 15^{\circ}, 20^{\circ}, 25^{\circ}, 15^{\circ} a n d 30^{\circ}$ respectively, Given, $∠ a + ∠ b + ∠ c + ∠ d + ∠ e + ∠ g = 270^{\circ} .$ Then find the measure of $∠ g$ and $∠ f$

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Solution

Given $∠ a + ∠ b + ∠ c + ∠ d + ∠ e + ∠ g = 270$
$∴ ∠ g = 270 - (∠ a + ∠ b + ∠ c + ∠ d + ∠ e) 270 - (15 + 20 + 25 + 5 + 30) = ∠ g ∠ g = 270 - 105 = 165$

From the figure we infer $∠ a + ∠ b + ∠ c + ∠ d + ∠ e + ∠ f + ∠ g$ is angle around a point, that is, angle around a point $= 360^{\circ}$
$∴ ∠ a + ∠ b + ∠ c + ∠ d + ∠ e + ∠ g + ∠ f = 360^{\circ} ∴ ∠ f = 360^{\circ} - (∠ a + ∠ b + ∠ c + ∠ d + ∠ e + ∠ g) = 360^{\circ} - 270^{\circ} (g i v e n) ∠ f = 90^{\circ}$

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