Math, asked by Anonymous, 6 months ago

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.​

Answers

Answered by Anonymous
1010

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

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}

Similar questions