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

Explanation:

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

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.

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

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.

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

$\boxed{ \sf \blue{ suppose\: the \: angles \: be \: 2x \: and\: 3x }}$

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

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

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

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

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

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

Answer 2

Answer:

Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2.

Let ∠A = 3x and ∠B = 2x

We know that the sum of the measures of adjacent angles is 180º for a parallelogram.

∠A + ∠B = 180º

3x + 2x = 180º

5x = 180º

x = 180/5 = 36 degree

∠A = ∠C = 3x = 108º (Opposite angles)

∠B = ∠D = 2x = 72º (Opposite angles)

Thus, the measures of the angles of the parallelogram are 108º, 72º, 108º, and 72º.