Question

please solve this problem in details​

Answer 1

• a, b and c are exterior angles. • x, y and z are interior angles.

As we know that the exterior angle of a triangle are equal to the sum of the two opposite interior

angles, therefore

• a = y+x

• b = y+z • c = x+z

So,

a+b+c = (y+x)+(y+z)+(x+z)

or, a+b+c = 2x + 2y +2z

or, a+b+c = 2(x+y+z)

As we know that the sum of all interior angles of a triangle is 180°, therefore

or, a+b+c = 2(180)

or, a+b+c = 2×180

or, a+b+c = 360

Kindly mark as brainliest.

Answer 2

Answer:

360*

Step-by-step explanation:

let us first equate the exterior angles to the interior angles.

acccording to the exterior angle sum property, An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles. The sum of the exterior angle and the adjacent interior angle that is not opposite is equal to 180º.

so, we can say-

∠a = ∠y + ∠x

∠b = ∠z + ∠y

∠c = ∠x + ∠z

and adding them becomes -

=> ∠a + ∠b + ∠c = (∠y + ∠x) + (∠z + ∠y) + (∠x + ∠z)

=> ∠y + ∠y + ∠z + ∠z + ∠x + ∠x

=> 2(∠y) + 2(∠z) + 2(∠x)

=> 2(∠y+∠z+∠x)

we know all the interior angles of the triangle adds upto 180*

so-

=> ∠y+∠z+∠x = 180*

=> 2(∠y+∠z+∠x) = 2(180) = 360

therefore-

=> ∠a + ∠b + ∠c =  2(∠y+∠z+∠x) = 360

=> ∠a + ∠b + ∠c = 360*