Question

the measurement of two adjacent angle of a parallelogram are in the ratio 3 ratio 2 find the measurement of each of the angle of the parallelogram​

Answer 1

$\large{\underline{\underline{\sf{ \maltese \: {Given:-}}}}}$

• The measures of two adjacent angles of a parallelogram = 3:2

$\large{\underline{\underline{\sf{ \maltese \: {To \: find:-}}}}}$

• The measure of each of the angles of the parallelogram = ?

$\large{\underline{\underline{\sf{ \maltese \: {Solution:-}}}}}$

Let the angles = 3x and 2x

~ We know that:–

$\qquad \bull \: { \bf {Adjacent \: angles \: of \: a \: parallelogram \: = 180 ^\circ}}$

$\qquad \quad{:} \longrightarrow \sf{3x + 2x = 180}$

$\qquad \quad{:} \longrightarrow \sf{5x = 180}$

$\qquad \quad{:} \longrightarrow \sf{x = \dfrac{180}{5} }$

$\qquad \quad{:} \longrightarrow \sf{x = \cancel\dfrac{180}{5} }$

$\qquad \quad{:} \longrightarrow \underline{ \boxed{\sf{x = 36 }}}$

~ Angles of the parallelogram:–

$\qquad \quad \blacksquare \: \sf{3x^\circ = \bigg( 3 \times 36 \bigg)^\circ = \underline{\underline{108^\circ}}}$

$\qquad \quad \blacksquare \: \sf{2x^\circ = \bigg( 2 \times 36 \bigg)^\circ = \underline{\underline{72^\circ}}}$

~ Verification:–

$\qquad \quad{:} \longrightarrow \sf{3x + 2x = 180}$

$\qquad \quad{:} \longrightarrow \sf{ \bigg(3 \times 36 \bigg) + \bigg(2 \times 36 \bigg) = 180}$

$\qquad \quad{:} \longrightarrow \sf{108 + 72 = 180}$

$\qquad \quad{:} \longrightarrow \underbrace{\sf{180= 180}}$

$\LARGE\underbrace{\bf{Hence \: Verified!!}}$

Answer 2

We know that ,

Opposite Sides of parallelogram are parallel...

So, the adjecent angle will be interior angles of the transversal....which has the sum 180°.

So, let 3x and 2x be the angles....

➜ 3x + 2x = 180°

➜ 5x = 180°

➜ x = 36°

So, the angles are ...

3x = 36 × 3 = 108°

2x = 2 × 36 = 72°

Now ,

We know ,

opposite angles of parallelegram are equal...

So, the angles of parallelogram are 108°,72°,108°,72°.