Find angle x and measure of each exterior angle of the given figure. [4 MARKS]

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Solution

Concept: 1 Mark
Application: 0.5 Mark each

We know that the sum of all exterior angles of a polygon is $360^{\circ}$

$∴ (2 x - 1)^{\circ} + (6 x + 4)^{\circ} + (4 x + 1)^{\circ} + (7 x - 2)^{\circ} + (8 x + 3)^{\circ} + (3 x - 5)^{\circ} = 360^{\circ}$

$\Rightarrow 30 x^{\circ} = 360^{\circ}$

$x = 12^{\circ}$

$∴$ First angle $= (2 x - 1)^{\circ} = (2 \times 12 - 1)^{\circ}$

$= 23^{\circ}$

Second angle $= (6 x + 4)^{\circ} = (6 \times 12 + 4)^{\circ}$

$= 76^{\circ}$

Third angle $= (4 x + 1)^{\circ} = (4 \times 12 + 1)^{\circ}$

$= 49^{\circ}$

Fourth angle $= (7 x - 2)^{\circ} = (7 \times 12 - 2)^{\circ}$

$= 82^{\circ}$

Fifth angle $= (8 x + 3)^{\circ} = (8 \times 12 + 3)^{\circ}$

$= 99^{\circ}$

Sixth angle $= (3 x - 5)^{\circ} = (3 \times 12 - 5)^{\circ}$

$= 31^{\circ}$

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Similar questions

How do we find the measure of EACH exterior angle and the measure of EACH interior angle of any polygon?

∠ A C D

A B C

∠ B = 40^{0}

∠ A = 70^{0}

∠ A C D

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