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

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

o

⇒3x+2x=180

o

⇒5x=180

o

⇒x=

5

180

o

=36

o

∴∠3×36

o

=108

o

and, ∠B=2×36

o

=72

o

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108

o

and ∠D=∠B=72

o

Hence, ∠A=108

o

,∠B=72

o

,∠C=108

o

and ∠D=72

o

Answer 2

$\begin{gathered}\begin{gathered}\\\\\sf \large \red{\underline{Given :-}}\\\\\end{gathered}\end{gathered}$

• The measures of two adjacent angles of a parallelogram are in the ratio 3:2.

$\begin{gathered}\begin{gathered}\\\\\sf \large \red{\underline{To \: Find:-}}\\\\\end{gathered}\end{gathered}$

• Find the measure of each of the angles of the parallelogram.

$\begin{gathered}\begin{gathered}\\\\\sf \large \red{\underline{Solution :- }}\\\\\end{gathered}\end{gathered}$

$\text{ \sf suppose the angles be equal to 3x and 2x}$

$\boxed{ \sf \orange{ we \: have \: adjacent \: angles \: of \: a \: parallelogram \: = 180}}$

$\begin{gathered}\begin{gathered}\\ \sf \underline{ \green{putting \: all \: values : }}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\: \\ \sf \to \: 3x + 2 x = 180\: \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:5x = 180 \\ \\ \: \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \frac{180}{5} \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \cancel{ \frac{180}{5} } \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \purple{x = 36}\\\\\end{gathered}\end{gathered}$

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

$\sf \large\underline{ \blue{verification }} \huge \dag$

$\begin{gathered}\begin{gathered}\\ \\ \sf \to 3x + 2x = 180 \\ \\ \sf \to \: 3 \times 36 +2 \times 36 = 180 \\ \\ \sf \to \: 108 + 72 = 180 \\ \\ \sf \to \:180 = 180 \\ \\ \large \underline{ \pink{ \sf \: hence \: verified}} \huge \dag\end{gathered}\end{gathered}$