Question

Prove that in a triangle, any exterior angle is larger than any of its remote interior angles.

a) The exterior angle equals the sum of two remote interior angles
b) The exterior angle is less than the sum of two remote interior angles
c) The exterior angle is equal to one remote interior angle
d) The exterior angle is greater than one remote interior angle

Answer 1

In a triangle, the exterior angle is equal to the sum of two remote interior angles.

Step-by-step explanation:

In a triangle, any exterior angle is larger than any of its remote interior angles. The exterior angle is equal to the sum of two remote interior angles. So option a) is correct.

To prove this, let's consider a triangle with three interior angles A, B, and C. The exterior angle, X, is formed by extending one of the sides of the triangle. The remote interior angles are A and B.

According to the Exterior Angle Theorem, the exterior angle X is equal to the sum of two remote interior angles A and B. In other words, X = A + B. Therefore, the exterior angle X is larger than any of its remote interior angles, and option a) is the correct answer.