Question

11. Two adjacent angles in a parallelogram are in the ratio 2:4. Find the values?
a. 80,100 b. 40,140 C. 60,120
c. 60,120 d. None of the above​

Answer 1

Given,

Two adjacent angles in a parallelogram are in the ratio 2:4.

To Find,

The value of these angles.

Solution,

→ Let the two adjacent angles of the parallelogram be 2x and 4x.

→ We know that the sum of the adjacent angles of a parallelogram is 180°.

→ So forming an equation:

2x + 4x = 180°

= 6x = 180°

∴ x = $\dfrac{180}{6}$

= 30

Therefore,

2x = 2 x 30 = 60°

4x = 4 x 30 = 120°

So, the two adjacent angles of the parallelogram have the measures 60° and 120°.

∴ Required option is Option C: 60 degrees and 120 degrees.

Knowledge Bytes:

→ Parallelogram

A parallelogram is a quadrilateral with opposite pairs of sides as equal and parallel.

→ Properties of a parallelogram

✳ The opposite pairs of sides are equal and parallel.

✳ The opposite angles are equal.

✳ The adjacent angles of a parallelogram are supplementary.

✳ The two diagonals of this quadrilateral bisect each other.

✳ It follows the parallelogram law, that is, the sum of the squares of the sides of parallelogram is equal to the sum of the squares of its diagonals.

These are the five basic properties of a parallelogram.