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

Step-by-step explanation:

Let the measure of two adjacent angle ∠A & ∠B of parallelogram ABCD are in the ratio 3:2.

Let ∠A=3x & ∠B=2x

We know sum of two adjacent angles of parallelogram is 180°

3x+2x=180°

5x=180[x=36° ]

Hence ∠A=3x=108° & ∠B=2x=72°

[∠A=∠C=180° ] & [∠B=∠D=72° ].

Answer 2

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

5. 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.

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

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

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

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

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

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

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

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

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

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

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

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