Question

in a polygon, the segment joining two non-consecutive vertices is called the
select one:
a. radius
b. diagonal
c. vertex
d. diameter

a triangle can have a maximum of how many non-acute angles?
select one:
a. 3
b. 1
c. 2
d. zero

Explanation:

1. For the first question: A radius is a segment from a circle's center to its edge; a vertex is a corner of a polygon; a diameter is a special chord of a circle. Only a diagonal is defined as a segment connecting two non-consecutive vertices of a polygon.
2. For the second question: The sum of interior angles in a triangle is $180^\circ$. A non-acute angle is $\geq90^\circ$. If there were 3 non-acute angles, their sum would exceed $180^\circ$. If there are 2 non-acute angles, their sum would be $\geq180^\circ$, leaving the third angle $\leq0^\circ$, which is impossible. Only 1 non-acute angle (obtuse or right) is possible, with the other two being acute angles whose sum adds to $180^\circ$ minus the non-acute angle.

Answer:

1. b. diagonal
2. b. 1