You are a botanist studying a rare flower. The center of the flower is a regular polygon. The petals coming off the flower are roughly triangular in shape. a. What is the name of the center polygon?
b. What is the sum of the interior angles of the center?
c. What is the measure of each interior angle of the center?
d. In order to compare the size of the petals to other flowers of the same species you need to determine the exterior angle of the polygon. What is the measure of the exterior angle of the polygon?

a). Regular Pentagon

b). 540°

c). 108°

d). 72°

Step-by-step explanation:

According To the Question

Given, a botanist studying a rare flower. The center of the flower is a regular polygon. The petals coming off the flower are roughly triangular in shape.

a). the name of the center polygon is Regular Pentagon

b). the sum of the interior angles of the Regular Pentagon is 540°

c). the measure of each interior angle of the Regular Pentagon is 108°

d). the measure of the Each exterior angle of the Regular pentagon is 72° & Sum of All Exterior Angle Of Regular Pentagon is 360°

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.