The outer angles of the triangle are in the ratio 4 : 5 : 6. Find the measure of the smallest angle.
96

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Solution

The correct option is A 96
Let the angles be $4 x$ , $5 x$ and $6 x$ .

The sum of the outer angles of the triangle is 360°

$∴ 4 x + 5 x + 6 x = 360 °$

$\Rightarrow 15 x = 360 °$

$\Rightarrow x = 24 °$

Hence the measure of the angles are
$4 x = 4 \times 24 = 96 ° 5 x = 5 \times 24 = 120 ° 6 x = 6 \times 24 = 144 °$

Therefore, the measure of smallest angle is 96°.

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