Question

The measures of two adjacent angles of a parallelogram are in the ratio 4 : 5 , find the measure of each of the angles of the parallelogram.
​

Answer 1

A parallelogram, being a quadrilateral has four interior angles. The neighbouring angles here are consecutive angles. A diagonal splits a vertex angle into the two; those are the adjacent angles.

Two consecutive angles are supplements; one acute, the other obtuse.

By data, they are in the ratio of 4:5 = 4x:5x.

So, 4x+5x = 180°

9x = 180°

x = 20°

4x = 80° and 5x = 100°

Hence, the consecutive angles in the parallelogram are 80° and 100°.

Answer 2

Question?

The measures of two adjacent angles of a parallelogram are in the ratio 4 : 5 , find the measure of each of the angles of the parallelogram.

Answer:-

Measure of both the angles are 80 and 100 degrees

Explanation:-

$\large { \underline{ \rm{Given }}}$

• The measures of two adjacent angles of a parallelogram are in the ratio 4 : 5

$\large { \underline{ \rm{To \: Find:-}}}$

• Measure of each of the angles of the parallelogram.

$\large { \underline{ \rm{Formula \: Used:- </p><p>}}}$

Sum of the adjacent angles in a parallelogram = 180

➪Ratio of adjacent angles = 4:5

${ \underline{ \rm{Let:- </p><p>}}}$

• First angle = 4x
• Second angle = 5x

$\implies \rm{4x+5x=180}$

$\implies \rm{9x=180}$

$\implies \rm{x= \frac{180}{90} }$

$\implies \rm{x= 20 }$

${ \underline{ \rm{Required \: Angles:- }}}$

➪First angle

$\implies \rm{4x= 4 \times 20 =80}$

➪Second angle

$\implies \rm{5x= 5 \times 20 =100}$

$\large{ \pink{ \boxed{ \rm{Hence, Measure \: of \: both \: the \: angles \: are \: 80 \: and \: 100 d \: egrees}}}}$