Question

I if two angles of a quadrilateral are supplementary the other two are in 4 is to 5 ratio then they are?

Answer 1

Solution :

Here, are two supplementary angles in the ratio 4 : 5.

Let

• first supplementary angle be 4x
• second supplementary angle be 5x

We know that, sum of supplementary angles is 180°.

Now, according to question :

=> 4x + 5x = 180°

=> 9x = 180°

=> x = 180/9

=> x = 20

Now, multiply the ratio by 20.

• first supplementary angle => 4x = 4 × 20 = 80°
• second supplementary angle => 5x = 5 × 20 = 100°

Hence, the supplementary angles are 80° and 100° respectively.

Answer 2

Question :

If two angles of a quadrilateral are supplementary the other two are in 4 is to 5 ratio then they are?

Given :

• Two angles of quadrilateral are supplementary.
• Other two angles are in ratio 4:5.

To find :

• Measure of the two angles.

Solution :

It is given that the two angles of quadrilateral are supplementary. This means that the other two angles will also be supplementary because sum of all the angles of quadrilateral is 360° .

• Let one angle = 4x

• Other angle = 5x

$\tt \star{4x + 5x = 180°}$

$: \implies \tt {9x = 180°}$

$: \implies \tt {x = \dfrac{180}{9}}$

$: \implies \tt {x = 20 }$

$\tt { One \: angle \: = 4x = 4(20) = 80° }$

$\tt {Other \: angle \: = 5x = 5(20) = 100 °}$