Question

Can a triangle have an exterior angle that measures 90° at two different vertices?

Answer 1

Answer:

NO

Step-by-step explanation:

A triangle at most can be a right triangle.

Answer 2

The exterior angle of a triangle is formed by extending one sides of the triangle.

A triangle cannot have an exterior angle that measures 90° at two different vertices

If the exterior angle of a triangle measure 90 degrees, at two vertices.

Then, it means that, the triangle is right-angled at two points

So, the third angle of the triangle would be:

$\mathbf{\theta + 90 + 90 = 180}$

$\mathbf{\theta + 180 = 180}$

Subtract 180 from both sides

$\mathbf{\theta = 0}$

The third angle of the triangle is 0 degrees.

The above highlights are not possible for a valid triangle, because the smallest angle of a triangle must be:

$\mathbf{\theta > 0}$

Hence, a triangle cannot have an exterior angle that measures 90° at two different vertices

Read more about exterior angles of a triangle at:

https://brainly.com/question/4164600