91Ó°ÊÓ

Find the measure of an exterior angle of each of the following equiangular polygons. a A triangle b A quadrilateral c An octagon d A pentadecagon e A 23 -gon

The measures of the three angles of a triangle are in the ratio \(4: 5: 6 .\) Find the measure of each.

Find the sum of the measures of the exterior angles, one per vertex, of each of these polygons. a A triangle b A heptagon c A nonagon d A 1984-gon

What is the fewest number of sides a polygon can have?

In an equiangular polygon, the measure of each exterior angle is \(25 \%\) of the measure of each interior angle. What is the name of the polygon?

a) Prove that the perpendicular bisector of a side of a regular pentagon passes through the opposite vertex. b) Can you generalize about the perpendicular bisectors of the sides of regular polygons?

On a clock a segment is drawn connecting the mark at the 12 and the mark at the 1 ; then another segment connecting the mark at the 1 and the mark at the \(2 ;\) and so forth, all the way around the clock. a What is the sum of the measures of the angles of the polygon formed? b What is the sum of the measures of the exterior angles, one per vertex, of the polygon?

Tell whether each statement is true Always, Sometimes, or Never \((\mathrm{A}, \mathrm{S}, \text { or } \mathrm{N})\) a. The acute angles of a right triangle are complementary. b. The supplement of one of the angles of a triangle is equal in measure to the sum of the other two angles of the triangle. c. A triangle contains two obtuse angles. d. If one of the angles of an isosceles triangle is \(60^{\circ},\) the triangle is equilateral. e. If the sides of one triangle are doubled to form another triangle, each angle of the second triangle is twice as large as the corresponding angle of the first triangle.

Prove that corresponding altitudes of congruent triangles are congruent.

The vertex angle of an isosceles triangle is twice as large as one of the base angles. Find the measure of the vertex angle.