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:

Let the adjacent sides be 3x and 2x,

we know that sum of adjacent sides of parallelogram is 180 degree.

So, 3x + 2x = 180

5x = 180

x = 36

Therefore, 3x = 108 degree

2x = 72 degree.

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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.

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

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

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

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

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

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

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

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