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

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

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.

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

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

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

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

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

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

†

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

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

Answer 2

$\huge \pink{\mathbb {Answer ツ}}$

Let us take the two adjacent angles be 3x & 2x

Note :- Sum of the adjacent angles in a parallelogram is 180°

So, we will simply add up and equal to 180 and will get the value of x

→ 3x + 2x = 180

→ 5x = 180

→ x = 180/5

→ x = 36

Thus, we got the value of x which is 36

Now, we will simply subsitute the values

1st angle :- 3x = 3 × 36 = 108

2nd angle :- 2x = 2 × 36 = 72