Question

adjacent angles of a parallelogram are in the ratio 2:3 find the measures of the angles of a parallelogram​

Answer 1

Answer:

Given :-

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

To Find :-

• What is the measures angles of a parallelogram.

Solution :-

Let,

$\mapsto \bf First\: Angle_{(Parallelogram)} =\: 2x$

$\mapsto \bf Second\: Angle_{(Parallelogram)} =\: 3x$

As we know that :

$\footnotesize \: \: \bigstar \: \: \sf\boxed{\bold{Sum\: of\: two\: adjacent\: angles_{(Parallelogram)} =\: 180^{\circ}}}\: \: \: \bigstar$

So, according to the question by using the formula we get,

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

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

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

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

Hence, the required adjacent angles of a parallelogram are :

$\dag$ First Angle Of Parallelogram :

$\dashrightarrow \sf First\: Angle_{(Parallelogram)} =\: 2x$

$\dashrightarrow \sf First\: Angle_{(Parallelogram)} =\: 2 \times 36^{\circ}$

$\dashrightarrow \sf\bold{\underline{First\: Angle_{(Parallelogram)} =\: 72^{\circ}}}$

$\dag$ Second Angle Of Parallelogram :

$\dashrightarrow \sf Second\: Angle_{(Parallelogram)} =\: 3x$

$\dashrightarrow \sf Second\: Angle_{(Parallelogram)} =\: 3 \times 36^{\circ}$

$\dashrightarrow \sf\bold{\underline{Second\: Angle_{(Parallelogram)} =\: 108^{\circ}}}$

$\therefore$ The measures of adjacent angles of a parallelogram is 72° and 108° respectively.

Answer 2

Given:-

• Ratio of two adjacent angles is = 2:3

To find:-

• The measure of those angles.

Solution:-

★We can assume that the measure of angles be "x" and we also know that the sum of adjacent angles of a parallelogram is 180°.★

$\sf{\longmapsto Let \: the \: measure \: of \: angle \: be \: \red{x}}$

$\sf{ \longmapsto Measure \: of \: {1}^{st} angle = 2x}$

${\sf{ \longmapsto Measure \: of {2}^{nd} \: angle = 3x}}$

»»»We know that the sum of adjacent angles is 180°.«««

Hence,

$\large \underline{\sf{ \implies 2x + 3x = 180 \degree}}$

$\large\underline{\sf{ \implies 5x = 180 \degree}}$

$\large\underline{\sf{ \implies x= \frac{180 \degree}{5} }}$

$\large \blue{\underline{ \green {\boxed{\sf{ \red{ \: \: \: \: \: \: \: \: \: \: \implies x = 36 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: }}}}}}$

Calculating for angles:-

$\large \blue{\underline{ \green {\boxed{\sf{ \red{ \implies2x = 2 \times 36 \degree = 72 \degree}}}}}}$

$\large \blue{\underline{ \green{ \boxed{\sf{ \red{ \implies3x = 3 \times 36 \degree = 108 \degree}}}}}}$

______________________________________

Verification:-

We know that sum of interior angles of a quadrilateral(parallelogram) is 360°.

$\large\underline{\sf{ \implies{2 \times (72 \degree + 108 \degree)}}}$

$\large\underline{\sf{ \implies2 \times 180 \degree}}$

$\large \blue{\underline{ \green{ \boxed{ \sf{ \red{ \implies360 \degree}}}}}}$

Hence verified!!

Henceforth the value of the adjacent angles in ratio 2:3 is (72° and 108°).