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,

$\dfrac{5}{4}=\dfrac{5.39}{a}$

$1.25=\dfrac{5.39}{a}$

$a=\dfrac{5.39}{1.25}$

$a=4.312$

Similarly,

$\dfrac{5}{4}=\dfrac{5.83}{b}$

$1.25=\dfrac{5.83}{b}$

$b=\dfrac{5.83}{1.25}$

$b=4.664$

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