Question

use the figure and given information below. Show the calculations that lead to your results. Given: Polygon ROTFL ~ Polygon SUBAG Perimeter of ROTFL is 52. a) Find m∠G. (1 pt) b) Find AG. (2 pts) c) Find the perimeter of Polygon SUBAG. (2 pts)

Answer 1

Answer:

a) $\angle G = 125^\circ$

b) AG = 15 units

c) Perimeter of polygon SUBAG = 78 units

Step-by-step explanation:

Given:

Polygon ROTFL ~ Polygon SUBAG

Similar polygons mean they have similar angles and the ratio of corresponding sides and ratio of their perimeter are equal.

Part A:

Given that

$m\angle R = 100^\circ\\m\angle O = 120^\circ\\m\angle T = 75^\circ\\M\angle L = 60^\circ$

$m\angle L+M\angle L = 180^\circ\\\Rightarrow m\angle L=180-60=120^\circ$

Sum of all interior angles of a pentagon is $540^\circ$

$m\angle R+m\angle O+m\angle T+m\angle F+m\angle L=540^\circ\\\Rightarrow 100+120+75+m\angle F+120=540^\circ\\\Rightarrow m\angle F=125^\circ$

Due to similarity property of the two pentagons, $\angle F =\angle G = 125^\circ$

Part B:

Ratio of corresponding sides is equal.

Given the sides SU = 12, RO = 8 and FL = 10 units respectively.

$\dfrac{SU}{RO}=\dfrac{AG}{FL}\\\dfrac{12}{8}=\dfrac{AG}{10}\\\Rightarrow AG = 15\ units$

Part C:

Ratio of corresponding sides must be equal to ratio of perimeter of the two polygons:

$\dfrac{RO}{SU} = \dfrac{\text{perimeter of ROTFL}}{\text{perimeter of SUBAG}}\\\Rightarrow \dfrac{8}{12} = \dfrac{52}{\text{perimeter of SUBAG}}\\\Rightarrow \text{perimeter of SUBAG} = 52 \times 1.5\\\Rightarrow \text{perimeter of SUBAG} = 78\ units$

So, the answers are:

a) $\angle G = 125^\circ$

b) AG = 15 units

c) Perimeter of polygon SUBAG = 78 units