The measures of the angles of a triangle are x+2, x+4, and 2x+10. How do you find the measure of each angle?

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The measures of the angles of a triangle are x+2, x+4, and 2x+10. How do you find the measure of each angle?

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Answer 1 · 2017-06-12T07:51:08

$43^{\circ}, 45^{\circ}, 92^{\circ}$ $43^@, 45^@, 92^@$

Explanation:

In a triangle, the three interior angles always add up to $180^{\circ}$ $180^@$

Let the three angles of the triangle be $(x + 2), (x + 4) and (2 x + 10)$ $(x+2), (x+4) and (2x+10)$ , respectively.

$\Rightarrow (x + 2) + (x + 4) + (2 x + 10) = 180^{\circ}$ $=> (x+2)+(x+4)+(2x+10)=180^@$
$\Rightarrow 4 x + 16 = 180$ $=> 4x+16=180$
$\Rightarrow x = \frac{180 - 16}{4} = 41^{\circ}$ $=> x=(180-16)/4=41^@$

Hence,
$x + 2 = 41 + 2 = 43^{\circ}$ $x+2=41+2=43^@$
$x + 4 = 41 + 4 = 45^{\circ}$ $x+4=41+4=45^@$
$2 x + 10 = 2 \times 41 + 10 = 92^{\circ}$ $2x+10=2xx41+10=92^@$

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The measures of the angles of a triangle are x+2, x+4, and 2x+10. How do you find the measure of each angle?

1 Answer

Explanation:

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