Question

The measure of two adjacent angles of a parallelogram are in the ratio 5:4. Find the measure of all its angles​

Answer 1

Step-by-step explanation:

Let the angles be 5x and 4x

The sum of the adjacent angles of parallelogram is 180

5x+4x = 180

9x=180

x=180/9

x=20 so 5x is equal to 5 multiply 20 that is 100degree

4x is equal to 4 multiply 20 that is 80 degree

Let other two angles by angle 1 and angle 2

angle 1 is equal to 100degree and angle 2 80 degree

Answer 2

Answer:

$\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \: \angle \:A = \angle \:C=100\degree\qquad \: \\ \\& \qquad \:\sf \: \angle \:B = \angle \:D=80\degree \end{aligned}} \qquad \:$

Step-by-step explanation:

Given, measure of two adjacent angle of a parallelogram are in the ratio 5:4.

Let assume that ABCD be a parallelogram such that

$\sf \: \angle \: A : \angle \:B \: = \: 5 : 4$

We know, sum of adjacent angles of a parallelogram is 180°.

So, using this property of parallelogram, we get

$\sf \: \angle \:A + \angle \:B = 180 \degree$

$\sf \: 5x + 4x = 180 \degree$

$\sf \: 9x= 180 \degree$

$\sf\implies \sf \: x= 20 \degree$

So,

$\sf\implies \sf \: \angle \:A = 5 \times 20 = 100\degree$

and

$\sf\implies \sf \: \angle \:B = 4 \times 20 = 80\degree$

Further, we know that opposite angles of a parallelogram are equal.

So, using this property of parallelogram, we get

$\sf\implies \sf \: \angle \:A = \angle \: C= 100\degree$

$\sf\implies \sf \: \angle \:D = \angle \: B= 80\degree$

Hence,

$\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \: \angle \:A = \angle \:C=100\degree\qquad \: \\ \\& \qquad \:\sf \: \angle \:B = \angle \:D=80\degree \end{aligned}} \qquad \:$