#### QUESTION

#### Measures of opposite angles of a parallelogram are (3x − 2)° and (50 − x)° . Find the measure of its each angle.

#### SOLUTION

Let ₹PQRS be the parallelogram.

m∠Q = (3x – 2)° and m∠S = (50 – x)°

m∠Q = m∠S

…..(i)

[Opposite angles of a parallelogram are congruent]

∴ 3x – 2 = 50 – x

∴ 3x + x = 50 + 2

∴ 4x = 52

∴ x = 524

∴ x = 13

Now, m∠Q = (3x – 2)°

= (3 x 13 – 2)° = (39 – 2)° = 37°

∴ m∠S = m∠Q = 37° …[From(i)]

m∠P + m∠Q = 180°

….[Adjacent angles of a parallelogram are supplementary]

∴ m∠P + 37° = 180°

∴ m∠P = 180° – 37° = 143°

∴ m∠R = m∠P = 143°

…..[Opposite angles of a parallelogram are congruent]

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

Let ₹PQRS be the parallelogram.

m∠Q = (3x – 2)° and m∠S = (50 – x)°

m∠Q = m∠S

…..(i)

[Opposite angles of a parallelogram are congruent]

∴ 3x – 2 = 50 – x

∴ 3x + x = 50 + 2

∴ 4x = 52

∴ x =

∴ x = 13

Now, m∠Q = (3x – 2)°

= (3 x 13 – 2)° = (39 – 2)° = 37°

∴ m∠S = m∠Q = 37° …[From(i)]

m∠P + m∠Q = 180°

….[Adjacent angles of a parallelogram are supplementary]

∴ m∠P + 37° = 180°

∴ m∠P = 180° – 37° = 143°

∴ m∠R = m∠P = 143°

…..[Opposite angles of a parallelogram are congruent]

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