Question

MNPQ ~ RSTU. What are the values of c,y and z. Please show work too.

Answer 1

x = 15 , y = 9 , z = 115°

Explanation:

since the figures are similar then the ratios of corresponding sides are in proportion, that is

`(NP)/(ST)` =
`(MN)/(RS)` ( substitute values )

`(x)/(25)` =
`(18)/(30)` ( cross- multiply )

30x = 450 ( divide both sides by 30 )

x = 15

and

`(TU)/(PQ)` =
`(MN)/(RS)` ( substitute values )

`(y)/(15)` =
`(18)/(30)` ( cross- multiply )

30y = 270 ( divide both sides by 30 )

y = 9

the corresponding angles in similar figures are congruent , so

∠ M = ∠ R , that is

z = 115°