# The angles of a triangle are in the ratio 1:3:5. What is the measure, in degrees, of the largest angle?

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vinit Share
Dec 3, 2015

we know that the sum of angles of the triangle is color(red)(180^@
lets say any angle is $x$

#### Explanation:

now as the angles are in ratio of $1 : 3 : 5$, we multiply 1,3,5 by $x$
now angles are $x$, $3 x$,$5 x$
the sum pf these angles should be ${180}^{\circ}$
$\therefore x + 3 x + 5 x = {180}^{\circ}$
$\therefore 9 x = {180}^{\circ}$
$\therefore x = {180}^{\circ} / 9$
$\therefore x = {20}^{\circ}$
now the largest angle will be $5 x$
hence angles are,
$x = {20}^{\circ}$
$3 x = 3 \cdot \left({20}^{\circ}\right) = {60}^{\circ}$ and
$5 x = 5 \cdot \left({20}^{\circ}\right) = {100}^{\circ}$
now the largest angle among these is ${100}^{\circ}$
( you can check that sum of angles is ${20}^{\circ} + {60}^{\circ} + {100}^{\circ} = {180}^{\circ}$)

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