Question

These two polygons are similar. In the spaces below, enter the values of a, b, m

Answer 1

Given:

The two polygons are similar.

To find:

The value of
`a,\ b,\ m\angle C,\ m\angle D`.

Solution:

We know that the corresponding side of similar figures are proportional. So,

`(5)/(4)=(5.39)/(a)`

`1.25=(5.39)/(a)`

`a=(5.39)/(1.25)`

`a=4.312`

Similarly,

`(5)/(4)=(5.83)/(b)`

`1.25=(5.83)/(b)`

`b=(5.83)/(1.25)`

`b=4.664`

We know that the corresponding angles of similar figures are congruent and their measures are equal. So,

`m\angle C=99.2^\circ`

`m\angle D=149^\circ`

Therefore,
`a=4.312\text{ units},\ b=4.664\text{ units},\ m\angle C=99.2^\circ,\ m\angle D=149^\circ`.