Question

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

Answer 1

Answer:

108° and 72°

Step-by-step explanation:

we know that the sum of adjacent angle of llgm is equal to 180°.

therefore, 3x+2x=180

5x=180

X=36

hence, angles are 108° and 72°

Answer 2

Question:−

Question:−

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.

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

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

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

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

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

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

$\boxed{ \sf \purple{ we \: have \: ardjacent \: angles \: of \: a \: parallelogram \: = 180}} \\ </p><p></p><p> </p><p> </p><p></p><p>\begin{gathered}\\ \sf \underline{ \purple{putting \: all \: values : }}\end{gathered} \\ </p><p> </p><p> </p><p> </p><p> </p><p></p><p>\begin{gathered}\: \\ \sf \to \: 3x + 2 x = 180\: \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:5x = 180 \\ \\ \: \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \frac{180}{5} \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \cancel{ \frac{180}{5} } \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \purple{x = 36}\\\\\end{gathered} </p><p>$

$\begin{gathered}\sf \to \: 3x \\ \sf \to \: 3 \times 36 \\ \sf \to \purple{108 }\\ \\ \\ \sf \to \: 2x \\ \sf \to \: 2 \times 36 \\ \sf \to \orange{72} \\\end{gathered} \\ </p><p></p><p></p><p>\sf \large\underline{ \purple{verification }} \huge \dag \\ </p><p></p><p> </p><p> †</p><p></p><p>\begin{gathered}\\ \\ \sf \to 3x + 2x = 180 \\ \\ \sf \to \: 3 \times 36 +2 \times 36 = 180 \\ \\ \sf \to \: 108 + 72 = 180 \\ \\ \sf \to \:180 = 180 \\ \\ \large \underline{ \purple{ \sf \: hence \: verified}} \\ \huge \dag\end{gathered} </p><p></p><p>$