Question

17 which of the following conjectures is illustrated by the diagram?

a the sum of the measures of the interior angles of a triangle is 180°.
b the base angles of an isosceles triangle are congruent.
c a point that lies on a perpendicular bisector of a line segment is equidistant from the line segments endpoints.
d the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Explanation:

• Option A: The sum of interior angles of a triangle is \(m\angle1 + m\angle2 + m\angle3=180^{\circ}\), which is not related to \(m\angle4\).
• Option B: There is no information indicating the triangle is isosceles.
• Option C: The diagram has nothing to do with a perpendicular bisector.
• Option D: \(\angle4\) is an exterior angle of the triangle. By the exterior - angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent (remote) interior angles. Here, \(m\angle4=m\angle1 + m\angle2\) (where \(\angle1\) and \(\angle2\) are the remote interior angles with respect to \(\angle4\)).

Answer:

D. The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.