Question

Given that A+B=C and angle between A and B is 150 degree if modeA= modeB

Answer 1

Answer:

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.

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

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}

Solution:−

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

\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}

puttingallvalues:

\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}

→3x+2x=180

→5x=180

→x=

5

180

→x=

5

180

→x=36

\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

†

\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}

→3x+2x=180

→3×36+2×36=180

→108+72=180

→180=180

henceverified

†