Question

Two opposite angles of a parallelogram are (3x -2) and (50-x). Find angles

ABCD is a cyclic quadrilateral, if < = 55°, find < .​

Answer 1

Question :-

Two opposite angles of a parallelogram are (3x - 2) and (50 - x). Find all the angles of parallelogram.

Answer :-

We know that,

Opposite angle of parallelogram are same.

So,

➩ 3x - 2 = 50 - x

➩ 3x + x = 50 + 2

➩ 4x = 52

➩ x = 52/4

➩ x = 13

Angle = 50 - 13 = 37°

We also know that,

Sum of adjacent angles of parallelogram sums up to 180°.

Let Adjacent angle be y

➩ y + 37 = 180°

➩ y = 180 - 37

➩ y = 143°

Angles of Parallelogram are 37° , 143° , 37° and 143°.

Answer 2

Given :-

• Two opposite angles of a Parallelogram are (3x - 2) and (50 - x). Find all the angles of parallelogram.

To find :-

★ We know that ★

Opposite angle of parallelogram are same.

So,

→ 3x - 2 = 50 - x

→ 3x + x = 50 + 2

→ 4x = 52

→ x = 52/4

→ x = 13

Solution :-

Angle = 50 - 13 = 37°

★ We also know that ★

• Sum of adjacent angeles of parallelogram sums up to 180°.

Let Adjcent angle be y

→ y + 37 = 180°

→ y = 180° - 37

→ y = 143°

Hence,

• Angle of Parallelogram are 37° , 143° , 37° and 143°.