\begin{tabular}{l|l|}\hline \( \begin{array}{l}\text { Sample Response: Because vertical angles are } \\ \text { congruent, angles } 1 \text { and } 4 \text { are congruent. Because } \\ \text { corresponding angles are congruent, angles } 4 \text { and } 8 \text { are } \\ \begin{array}{l}\text { congruent. Because angle } 4 \text { is congruent to both } 1 \text { and } 8, \\ \text { angle } 1 \text { is congruent to angle } 8 .\end{array}\end{array} \) & \( \begin{array}{l}\text { What did you include in your response? Check all that } \\ \text { apply. } \\ \square \text { vertical angles theorem } \\ \square \text { corresponding angles theorem } \\ \square \text { transitive property }\end{array} \) \\ \( \square \) supplementary angles \\ \( \square \) linear pairs \end{tabular}

Case Study Based Question There was a deserted land near Ryan's house. The colony people used to throw garbage on that land. Ryan, along with his friends, decided to develop the land into a park with walking track with uniform width, where children can play and elders can work. On the basis of above information answer the following questions: (a) What is the width of the track? (b) Find the breadth of inner rectangle. (c) Find the area of walking track. (d) Find the cost of leveling the park including the track at the rate 210 per square m . (e) Which values Ryan has shown here?

Find the volume of the pyramid with base in the plane \( z=-5 \) and sides formed by the three planes \( y=0 \), and \( y-x=1 \) and \( x+y+z=0 \). NotE: Enter the eroct answer.

A fish tank length, breadth and height is \( 40 \mathrm{~cm}, 60 \mathrm{~cm} \) and 50 cm respectively. It contains 50 liter of water, How much water is needed to fill it completely.

5.20. In un rettangolo un lato misura 1 unità più dell'altro. Detta \( x \) la misura del lato minore, esprimi, in funzione di sharea di un quadrato che ha lo stesso perimetro del rettangolo.

1. A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside ar it. Find the area of the path. A path 5 m wide runs along inside a square park of side 100 m . Find the area path. A painting is painted on a cardboard 8 cm long and 5 cm wide such that the margin of 1.5 cm along each of its sides. Find the total area of the margin. The side of a square flower bed is 1 m 80 cm . It is enlarged by digging a strit wide all around it. Find: (i) the area of the enlarged flower bed