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

${ \underbrace{ \gray{ \mathfrak{Given : }}}}$

• The ratio of two adjacent angles of a parallelogram is 3 : 2.

${ \underbrace{ \gray{ \mathfrak{ To \: find: }}}}$

↪ The measure of each of the angles of the parallelogram.

${ \underbrace{ \gray{ \mathfrak{Solution : }}}}$

We know that,

Two adjacent sides of a parallelogram is of 180°

${ \underbrace{ \gray{ \textbf{\textsf{Assuming : }}}}}$

The two sides as 3x and 2x.

$☯ \begin{gathered}\underline{\boldsymbol{According\: to \:the\: question :}}\\\end{gathered}$

$\sf \dashrightarrow 2x + 3x = 180 \degree$

$\sf \dashrightarrow 5x = 180 \degree \:$

$\sf \dashrightarrow x = \cancel{\frac{180}{5}}$

$\bf \dashrightarrow x = 36 \degree$

After solving we get :

x = 36°

Hence,

The other sides are :

2x = 2 × 36° = 72°

3x = 3 × 36° = 108°

$\therefore{ \underbrace{ \boxed{ \textbf{ \textsf{Required \: answer : }}}}} \\ { \underline{ \boxed{ \textbf{ \textsf{the \: two \: sides \: are \:72 \degree and \: 108 \degree }}}}}$

${ \underbrace{ \boxed{ \textbf{ \textsf{ \: Verification : }}}}}$

We know that,

Two adjacent angles are always equal to 180°

Therefore,

2x and 3x must be equal to 180°

↪2x + 3x = 180°

↪72° + 108° = 180°

↪180° = 180°

${\underline{\boxed{\bf{\green{Hence,}\purple{V}\orange{e}\green{r}\blue{i}\red{f}\pink{i}\gray{e} d }}}}$

Answer 2

Answer:

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

$∠A+∠B=180</strong></p><p></p><p></p><p><strong>[tex]∠A+∠B=180$

$⇒3x+2x=180</strong></p><p></p><p><strong>[tex]⇒3x+2x=180$

$⇒5x=180</strong></p><p></p><p><strong>[tex]⇒5x=180$

$⇒x=5 \div180o=36</strong></p><p></p><p></p><p><strong>[tex]⇒x=5 \div180o=36$

$∴∠3×36=108</strong></p><p></p><p><strong>[tex]∴∠3×36=108$

$and, ∠B=2×36=72</strong></p><p></p><p><strong>[tex]and, ∠B=2×36=72$

Since the opposite angles are equal in a parallelgram, therefore, 

$∠C=∠A=108 and ∠D=∠B=72</strong></p><p></p><p><strong>[tex]∠C=∠A=108 and ∠D=∠B=72$

$Hence, ∠A=108,∠B=72,∠C=108 and ∠D=72</strong></p><p></p><p><strong>[tex]Hence, ∠A=108,∠B=72,∠C=108 and ∠D=72$