Question

find the measure of angle x angle x measures 115° the measure of an exterior angle of any triangle equals a. the sum of the measures of the two remote interior angles b. 120 degrees. c. the measure of the adjacent interior angle d. 180° minus the measures of the two remote interior angles

Explanation:

The exterior angle theorem of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent (remote) interior angles. Option B is incorrect as an exterior angle doesn't have to be 120 degrees. Option C is wrong because an exterior angle and its adjacent interior angle are supplementary, not equal. Option D is incorrect as the formula for the exterior angle is the sum of the two remote interior angles, not related to 180° minus their sum (the sum of interior angles of a triangle is 180°, and the exterior angle is supplementary to the adjacent interior angle, so exterior angle = 180° - adjacent interior angle=(sum of two remote interior angles + adjacent interior angle)- adjacent interior angle = sum of two remote interior angles).

Answer:

A. The sum of the measures of the two remote interior angles