Question

The opposite angles of a parallelogram are (3x+5)° and (61-x)°. What are the Measure of the four angles?

Answer 1

Question:

The opposite angles of a parallelogram are (3x+5)° and (61-x)°. What are the Measure of the four angles?

Answer:

94°, 86°, 94°, 86°

Step-by-step explanation:

given that,

In a parallelogram,

opposite angles = (3x + 5)° and (61 - x)°

we know that,

In a parallelogram ,

opposite angles are equal,

DAB = BCD

so,

(3x + 5)° = (61 - x)°

by solving this,

3x - 5 = 61 - x

3x - x = 61 + 5

2x = 66

x = 66/2

x = 33

now,

given angle

3x - 5

3(33) - 5

99 - 5

94°

so,

DAB = BCD = 94°

In a parallelogram,

sum of adjecent angles = 180°

so,

ACCORDING TO THE FIGURE

DAB + ABC = 180°

94 + ABC = 180

ABC = 180 - 94

ABC = 86°

ABC = CDA = 86° [opposite angles]

so,

DAB = 94°

ABC = 86°

BCD = 94°

CDA = 86°

so,

________________________

Angles of the parallelogram are

94°, 86°, 94°, 86°

________________________

EXTRA INFORMATION

PARALLELOGRAM

Properties,

• for sided
• opposite sides are parallel
• unequal diagonals
• sum of angles = 360°
• opposite angles are equal
• sum of adjecent angles = 180°
• diagonal divides the parallelogram into to congruent triangles.

Area => base × height

perimeter => 2(length + breadth)

Answer 2

PARALLELOGRAM:

Given:

◼️PQRS is a parallelogram.

m( angle PQR) = 3x + 5°

m (angle PSR)  = 61 - x°

angle PQR & angle PSR are opposite angles of the parallelogram PQRS.

According to the property of parallelogram, which states:

Opposite angles of a parallelogram are congruent.

We get,

Angle PQR  = Angle  PSR i.e

(3x + 5)° = ( 61 - x) °

Find the value of x by solving the equation,

3x + 5 = 61 - x

3x + x = 61 - 5

4x = 56

x = 56/4

x = 14

The value of x has been carved out by solving the above equation, now substitute this value of x in 3x + 5 and get the value of the angle PQR in terms of digits.

3x + 5

= 3(14) + 5

= 42 + 5

= 47°

m( angle PQR)  = 47°

As we know the property of a parallelogram: opposite angles are congruent

m(angle PQR) = m (angle PSR)

.°. m(angle PSR)= 47°

As according  to another property of the parallelogram stating:

Adjacent angles of a parallelogram are supplementary

.°.m( angle PQR ) + m( angle QRS)  =180°

47° + m(angle QRS) = 180°

m(angle QRS) = 180 - 47

m (angle QRS) = 133°

Now,

m(angle SPQ) = m (angle QRS)=133°

(Opposite angles of a parallelogram are congruent)

m (angle SPQ) = 133°

.°. measure of four angles  of the parallelogram are :

1.m (angle PQR) =47°

2. m(angle QRS) =133°

3. m (angle PSR)  = 47°

4. m (angle SPQ) = 133°

Let's add all the angles and check whether we get the satisfied angle values or not.

m (angle PQR)+ m(angle QRS)+ m(angle PSR)+ m(angle SPQ) =360°

=> 47° + 133° + 47°+ 133° = 360°

=> 360° = 360°

Sum of all the angles of the parallelogram is 360° and we got the same after adding our answers.