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:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\purple{Given:}}}}}}}\end{gathered}$

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\purple{To Find:}}}}}}}\end{gathered}$

• ● The measure of each of the angles of the parallelogram.

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\purple{Solution:}}}}}}}\end{gathered}$

$\dag \: \underline{\frak{\red{Let \: the \: angles,}}}$

• ● 3x
• ● 2x

$\dag \: \underline \frak \red{As \: we \: know \: that}$

• The sum of any two adjacent angles of a parallelogram is equal to 180°.

$\dag \: {\underline{\frak{\red{According \: to \: the \: question}}}}$

$: \implies\sf{3x + 2x}= \bf{{180}^{\circ}}$

$: \implies\sf{5x}= \bf{{180}^{\circ}}$

$: \implies\sf{x}= \bf{\dfrac{180}{5}}$

$: \implies\sf{x}= \bf{\cancel{\dfrac{180}{5}}}$

$: \implies\sf{x}= \bf{{36}^{\circ}}$

$\dag\underline{\boxed{\rm{\pink{{x}={36}^{\circ}}}}}$

$\dag \: \underline{\frak{\red{Angles,}}}$

• ● 3×36 = 108⁰
• ● 2×36 = 72⁰

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\purple{Verification:}}}}}}}\end{gathered}$

$\dag \: \underline{\frak{\red{Checking \: our \: answer,}}}$

$: \implies\sf{3x + 2x}= \bf{{180}^{\circ}}$

• Substituting the angles

$: \implies\sf{{108}^{\circ} + {72}^{\circ} }= \bf{{180}^{\circ}}$

$: \implies\sf{{180}^{\circ}}= \bf{{180}^{\circ}}$

$\dag\underline{\boxed{\rm{\pink{LHS=RHS }}}}$

• ● Hence Verified ꪜ
• ● Henceforth,The our answer is correct..ꪜ

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\purple{Learn \: More:}}}}}}}\end{gathered}$

Adjacent Angles:

Any two angles that share

• ● a common ray or side
• ● a common vertex
• ● and whose interiors do not overlap

are called adjacent angles.

Answer 2

Answer:

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

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.

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

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

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

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

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

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

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

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

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