Question

An exterior angle of a triangle is 110 degree and its two interior opposite angles are in the ratio 2:3. Find the angles of the triangle

Answer 1

Exterior angle is sum of opposite interior angles
Let the angles be 2x,3x
So 2x+3x= 110
5x=110
x= 110/5
x= 22

So angle 2x = 44
3x = 66
And third angle is 180-44-66
= 180-110 = 70

Hope this helps

Answer 2

Answer:

Required three angles of the triangle are 70°,44°,66°

Step-by-step explanation:

Given,an exterior angle of a triangle is 110 degree and it's two interior oposite angles are in the ratio 2:3.

Let,First interior angle be 2x degree

Second interior angle be 3x degree

We know,sum of interior angles of a triangle is equal to exterior angle of the triangle.

For example if p degree and q degree are interior angle of a triangle and r degree is exterior angle of the triangle then we can say

$p + q = r$

Here two interior angles are 2x degree and 3x degree and exterior angle is 110°.

By the rule,

$2x + 3x = 110$

$5x = 110$

$x = \frac{110}{5}$

$x = 22$Therefore first angle of the triangle is $(2 \times 22) = {44}^{o}$

and second angle of the triangle is

$(3 \times 22) = {66}^{o}$

We know sum of all angles of a triangle is 180°.

So third angle of the triangle =180°-(44°+66°)=70°