If an angle of a parallelogram is two third of its adjacent angle then the angle measures degrees

If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram .

Let the measure of the angle be x

∴ The measure of the angle adjacent is  `(2x)/3`

We know that the adjacent angle of a parallelogram is supplementary

Hence x + `(2x) / 3` = 180°

2x + 3x = 540°

⇒ 5x = 540°

⇒ x = 108°

Adjacent angles are supplementary

⇒ x +108° = 180°

 ⇒ x =180° -108° = 72°

⇒ x = 72°

Hence, four angles are : 180°, 72°,108°, 72°

Concept: Angle Sum Property of a Quadrilateral

  Is there an error in this question or solution?

Answer

Read More

Vedantu Improvement Promise

>

If an angle of a parallelogram is two third of its adjacent angle, find the angles of the parallelogram.

Solution

Let in a parallelogram $ABCD$,

$\angle A=x$

Then its adjacent angle , $\angle B=\frac{2}{3}x$

But, $\angle A+\angle B={180}^{\circ }$ [Since, sum of the consecutive angles of a parallelogram is ${180}^{\circ }$.

$\Rightarrow x+\frac{2}{3}x={180}^{\circ }$

$\Rightarrow \frac{3x+2x}{3}={180}^{\circ }$

$\Rightarrow \frac{5x}{3}={180}^{\circ }$

$\Rightarrow x={180}^{\circ }\times \frac{3}{5}$

$\Rightarrow x={36}^{\circ }\times 3$

$\Rightarrow x={108}^{\circ }$

$\Rightarrow \angle A={108}^{\circ }$---(1)

$\Rightarrow \angle B={180}^{\circ }-{108}^{\circ }={72}^{\circ }$---(2)

Since, opposite angles of a parallelogram are equal.

$\Rightarrow \angle A=\angle C={108}^{\circ }$ ---(3)

and $\Rightarrow \angle B=\angle D={72}^{\circ }$---(4)

Hence angles are ${108}^{\circ },{72}^{\circ },{108}^{\circ },{72}^{\circ }$.

Mathematics

RD Sharma

Standard IX