Class 8 Maths

## Exercise 3.1 Part 2

Question 6: Find the angle measures x in the following figures.

Solution: We know that, angle sum of a quadrilateral = 360⁰
So, 50° + 130° + 120°+ x = 360°
Or, 300°+ x = 360°
Or, x = 360°- 300°= 60°

Question 6 (b)

Solution:

We know that, angle sum of a quadrilateral = 360⁰
So, 90° + 60°+ 70°+ x = 360°
Or, 220° + x = 360°
Or, x = 360°- 220°= 140°

Question 6 (c)

Solution:Solution

We know that angle sum of a pentagon = 540o
110° + 120° + 30° + x + x = 540°
Or, 260° + 2x = 540°
Or, 2x = 540° - 260° = 280°
Or, x = 280°÷2 = 140°

Question 6 (d)

Solution:Solution: Angle sum of a pentagon = (5 – 2) xx 180⁰ = 3 xx 180⁰ = 540⁰
Since, it is a regular pentagon, thus, its angles are equal
So, x + x + x + x + x = 540°
Or, 5x = 540°
Or, x = 540°÷5 = 108°

Question 7:

Solution:

We know that angle sum of a triangle = 180⁰
Thus, 30⁰ + 90⁰ + C = 180⁰
Or, 120⁰ + C = 180⁰
Or, C = 180⁰ – 120⁰
Or, C = 60⁰
Now, y = 180° - C
Or, y = 180° - 60° = 120°
Similarly, z = 180°- 30° = 150°
Similarly, x = 180° - 90° = 90°
Hence, x + y + z = 90° + 120° + 150°= 360°

Alternate method: We know that sum of external angles of a polygon = 360⁰
Hence, x + y + z = 180°

Solution:

We know that angle sum of a quadrilateral = 360⁰
A + 60° + 80° + 120° = 360°
Or, A + 260° = 360°
Or, A = 360° - 260° = 100°
Hence, w = 180° - 100° = 80°
Similarly, x = 180° - 120° = 60°
Similarly, y = 180° - 80° = 100°
Similarly, z = 180° - 60° = 120°
Hence, x + y + z + w = 60° + 100° + 120° + 80° = 360°

Alternate method: We know that sum of external angles of a polygon = 360⁰
Hence, x + y + z + w = 360°

## Rational Numbers

Any number which can be expressed in the form of p/q where q ≠ 0 is called rational number.

## Linear Equations

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

A plane figure bounded by a finite straight line segment in loop to form a closed chain is called a polygon.

## Data Handling

Learn about arranging data and making bar chart, histogram and pie chart.

## Probability

Probability of an outcome out of total events.

## Cube Roots

A number which is equal to another number raised to the power 3 is called a perfect cube.

## Algebraic Expressions

An expression with coefficient and variables is called algebraic expression.

## Mensuration

Learn to calculate area and perimeter of two-dimensional figures.

## Exponents Power

Exponents are used to represent a large number in simpler form.

## Proportion

A part compared to the whole is called proportion.

## Factorization

Factorization consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

## Graph

A graph is a pictorial representation of data to make it more user friendly.