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Answer 1

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

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.

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

Given:−

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

[tex[\begin{gathered}\begin{gathered}\\\\\sf \large \red{\underline{To \: Find:-}}\\\\\end{gathered}\end{gathered} [/tex]

ToFind:−

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

$\begin{gathered}\begin{gathered}\\\\\sf \large \red{\underline{Solution :- }}\\\\\end{gathered}\end{gathered} [/tex[</p><p>Solution:−</p><p> </p><p> </p><p> </p><p> </p><p> </p><p>suppose the angles be equal to 3x and 2x} suppose the angles be equal to 3x and 2x</p><p></p><p>[tex]\boxed{ \sf \orange{ we \: have \: ardjacent \: angles \: of \: a \: parallelogram \: = 180}}$

wehaveardjacentanglesofaparallelogram=180

$\begin{gathered}\begin{gathered}\\ \sf \underline{ \green{putting \: all \: values : }}\end{gathered}\end{gathered} ✓/tex]</p><p>puttingallvalues:</p><p> </p><p> </p><p> </p><p> </p><p> </p><p> </p><p></p><p>\begin{gathered}\begin{gathered}\: \\ \sf \to \: 3x + 2 x = 180\: \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:5x = 180 \\ \\ \: \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \frac{180}{5} \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \cancel{ \frac{180}{5} } \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \purple{x = 36}\\\\\end{gathered}\end{gathered} </p><p>→3x+2x=180</p><p>→5x=180</p><p>→x= </p><p>5</p><p>180</p><p> </p><p> </p><p>→x= </p><p>5</p><p>180</p><p> </p><p> </p><p> </p><p> </p><p>→x=36</p><p> </p><p> </p><p> </p><p> </p><p></p><p>\begin{gathered}\begin{gathered}\sf \to \: 3x \\ \sf \to \: 3 \times 36 \\ \sf \to \red{108 }\\ \\ \\ \sf \to \: 2x \\ \sf \to \: 2 \times 36 \\ \sf \to \orange{72} \\\end{gathered}\end{gathered}$

→3x

→3×36

→108

→2x

→2×36

→72

†

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

verification

†

[tex[\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} [/tex]

→3x+2x=180

→3×36+2×36=180

→108+72=180

→180=180

henceverified

†

†