Which theorem states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle?
A.
Triangle Sum Theorem
B.
Remote Interior Angle Theorem
C.
Exterior Angle Theorem
D.
Exterior Inequality Theorem
And does anyone know the rest of the answers as well?
Let me show you how it's done. Just go to Google and type in EACH of the answers and see what each theorem states. Pick the one that matches.
The theorem that states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle is called the Exterior Angle Theorem. To find the answer to this question, you can use your knowledge of geometry and specifically the properties of triangles.
To prove the Exterior Angle Theorem, you can start by drawing a triangle and extending one of its sides to create the exterior angle. The exterior angle is the angle formed by the extension of one of the sides of the triangle. Now, you have two interior angles and one exterior angle. By the Triangle Sum Theorem (option A), we know that the sum of the interior angles of a triangle is always 180 degrees. Therefore, the two remote interior angles of the triangle must add up to 180 degrees.
So, the correct answer is option C, the Exterior Angle Theorem.
As for the rest of the answers, the Triangle Sum Theorem (option A) states that the sum of the interior angles of a triangle is always 180 degrees. The Remote Interior Angle Theorem (option B) is not a real theorem; it was made up for this question. The Exterior Inequality Theorem (option D) is also not a real theorem and does not relate to the properties of triangles.