Math, asked by prashantbade141, 18 days ago

Practice Set 8.3 Measures of opposite angles of a parallelogram are (3x-2) and (50 - X). Find the measure of its each angle. 49

Answers

Answered by rudraprasadpattnaik9

Answer:

Maharashtra Board Class 8 Maths Solutions Chapter 8 Quadrilateral: Constructions and Types Practice Set 8.3

August 14, 2019 by Laxmi

Maharashtra State Board Class 8 Maths Solutions Chapter 8 Quadrilateral: Constructions and Types Practice Set 8.3

Question 1.

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)°

Maharashtra Board Class 8 Maths Solutions Chapter 8 Quadrilateral Constructions and Types Practice Set 8.3 1

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°.

Step-by-step explanation: