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Question #827f6

1 Answer

Jun 12, 2016

Largest angle: $100^{\circ}$ $100^@$

Explanation:

If the measure of the smallest angle is $a$ $a$
then the other two angles (given the $1 : 3 : 5$ $1:3:5$ ratio)
would be $3 a$ $3a$ and $5 a$ $5a$

We know that the sum of the angles of a triangle is $180^{\circ}$ $180^@$
So
$XXX a + 3 a + 5 a = 180^{\circ}$ $color(white)("XXX")a+3a+5a=180^@$
$\Rightarrow$ $rArr$
$XXX 9 a = 180^{\circ}$ $color(white)("XXX")9a=180^@$

$XXX a = 20^{\circ}$ $color(white)("XXX")a=20^@$

Since the largest angle is $5 a$ $5a$
the largest angle is $5 \times 20^{\circ} = 100^{\circ}$ $5xx20^@=100^@$

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