Question

find the value of each variable in the parallelogram. explain step by step /​

Answer 1

Answers:

Part A:

The figure is a parallelogram.

Property to be used - The opposite angles of a parallelogram are equal.

Forming an equation:

3m = 120°

m = 120/3

m = 40

Therefore the value of m is 40.

Part B:

The figure is a parallelogram.

Properties to be used:

→ Opposite sides of a parallelogram are equal and parallel.

→ The opposite angles of a parallelogram are equal.

Finding x:

x is opposite to the side of measure 6.

As per the first property.

x = 6

So, x = 6

Therefore the value of x is 6.

Finding y.

5y is opposite the angle measuring 45°.

Forming an equation.

5y = 45°

y = 45/5

y = 9

Therefore the value of y is 9.

★ Final answers:

m = 40

x = 6

y = 9

Parallelogram and Its Properties

→ A quadrilateral with opposite sides equal and parallel is known as a parallelogram. The properties of a parallelogram are listed below:

✳ The opposite sides are equal and parallel.

✳ The opposite angles have equal measure.

✳ The angles on the same side are supplementary.

✳ The two diagonals of a parallelogram bisect each other.

Answer 2

Answer:

• m = 40°

• x = 6

• y = 9°

Step-by-step explanation:

From Fig (e)

Property Used

• Opposite Angles of a parallelogram are equal.

• Here the opposite Angles are 3m,120

• So, 3m = 120

• $\tt m = \frac{120}{3}$

• $\tt{\boxed {m = 40^{\circ}}}$

From Fig (f)

Property's Used

• Opposite Angles of a parallelogram are equal.

• Opposite Sides of a Parallelogram are equal.

Firstly Let's Find x

• We know that Opposite Sides of a Parallelogram are equal.

• Opposite Sides are 6 ,x

• 6 = x

Secondly Let's find y

• We know that Opposite Angles of a parallelogram are equal.

• Opposite angles are 5y,45

• So, 5y = 45

• $\tt y = \frac{45}{5}$

• $\tt y = 9^{\circ}$