Question

measure of opposite angles of a parallelogram are (3x-2)^0 and (50-x)^0.find the measure of its each angle​

Answer 1

Answer:

The measures of the angles of the parallelogram are 37°, 37°, 143° and 143°.

Step-by-step-explanation:

We have given that,

The measures of two opposite angles of a parallelogram are ( 3x - 2 )° and ( 50 - x )°.

We have to find the measures of all the angles.

Now, we know that,

Opposite angles of a parallelogram are congruent.

∴ ( 3x - 2 )° = ( 50 - x )°

⇒ 3x - 2 = 50 - x

⇒ 3x + x = 50 + 2

⇒ 4x = 52

⇒ x = 52 ÷ 4

⇒ x = 13

Now,

First angle is ( 3x - 2 )°

∴ ( 3x - 2 ) = 3 * 13 - 2

⇒ ( 3x - 2 ) = 39 - 2

⇒ ( 3x - 2 ) = 37

∴ First angle = 37°

Now,

Second angle = First angle - - [ Opposite angles of parallelogram ]

∴ Second angle = 37°

Now, we know that,

Adjacent angles of a parallelogram are supplementary.

First angle + Third angle = 180°

⇒ 37° + Third angle = 180°

⇒ Third angle = 180 - 37

⇒ Third angle = 143°

Now,

Third angle = Fourth angle - - [ Opposite angles of parallelogram ]

∴ Fourth angle = 143°

∴ The measures of the angles of the parallelogram are 37°, 37°, 143° and 143°.

Answer 2

Given :

• Measure of two opposite angles of the parallelogram i.e. (3x - 2)° and ( 50 - x) °

To Find:

• All angles of the parallelogram.

Solution:

[ Opposite angles of a parallelogram are equal ]

⟹ (3x - 2)° = ( 50 - x)°

⟹ 3x + x = 50 + 2

⟹ 4x = 52

⟹ x = 52/4

⟹ x = 13

First angle = ( 3x - 2)° = { 3(13) - 2)° = 37°

Second angle = First angle = 37°

(opposite angles of a parallelogram are equal)

[ Adjacent angles of a parallelogram add up to 180° ]

let the third angle be y

⟹ 37° + y = 180°

⟹ y = 180° - 37°

⟹ y = 143°

Third angle = y = 143°

Forth angle = Third angle = 143°

(opposite angles of a parallelogram are equal)

Measure of the angles of the parallelogram : 37°, 37°, 143°, 143°.