Question

The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.​

Answer 1

Answer:

3x+2x=180

→5x=180

→x=

5

180

→x=

5

180

$\begin{gathered}\begin{gathered}\sf \to \: 3x \\ \sf \to \: 3 \times 36 \\ \sf \to \red{108 }\\ \\ \\ \sf \to \: 2x \\ \sf \to \: 2 \times 36 \\ \sf \to \orange{72} \\\end{gathered}\end{gathered}$

Answer 2

Answer:

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180

⇒3x+2x=180o

⇒5x=180

⇒x=5180o=36

∴∠3×36o=108o

and, ∠B=2×36o=72o

Since the opposite angles are equal in a parallelgram, therefore, 

∠C=∠A=108o and ∠D=∠B=72o

Hence, ∠A=108o,∠B=72o,∠C=108o and ∠D=72o