Question

One of the exterior angle of a triangle is 105° and the interior opposite angles are in the ratio 2:5. Find the angles of the triangle.

Answer 1

1st Angle= 30°
2nd Angle= 75°


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Answer 2

The Interior angles of the triangle are $30^{0} ,75^{0}$

Step-by-step explanation:

Given In a triangle exterior angle of a triangle is $105^{0}$

Interior opposite angles are in the ratio 2: 5

Let interior opposites angles are $2\textrm {x} \textrm{and} \textrm{5x}$

We know in a triangle exterior angle is equal to sum of two interior opposite angles

so $2\textrm{x}+5\textrm{x}=105^{0}$

$\Rightarrow 7\textrm{x}=105^{0}$

$\Rightarrow \textrm{x}=\dfrac {105^{0} }{7}$

$\Rightarrow \textrm{x}=15^{0}$

One interior angle is $2\textrm{x}=2\times15^{0} =30^{0}$

and other interior angle is $5\textrm{x}=5\times 15^{0} =75^{0}$