Exterior Angles in Polygon and Triangle

Exterior Angle
Consider a shape such as square ABCD. Extend the horizontal bottom of the square at the point D up to F. Now we have a vertical line BD and a horizontal line DF joining at the common vertex D. The angle BDF formed between the original side BD of the mathematical shape i.e. square and the extended side DF is termed to be the exterior angle. The angle formed on the inner side of BD is the interior angle BDC.  The sum of the interior angle and the exterior angle formed using the side BD is 180 degrees. This forms a horizontal straight line CF measuring 180 degrees.

Polygon
A mathematical shape which has straight sides and flat shape is termed to be polygon.

Exterior Angles Polygon
Exterior Angles Polygon definition states that: With one of the angles of the polygon, a linear pair is formed by an angle which is termed as an exterior angle of the polygon.

At every vertex of a polygon, two exterior angles can be formed at the maximum.  Each exterior angle of a polygon is formed in between a side of the polygon and the line extended from its adjacent side.

Finding Exterior Angles of Polygons
We can find the exterior angles formula for polygons. The important point to be noted here is that at each vertex of the polygon, two equal exterior angles can be drawn but the formula for finding the exterior angles of polygon uses only one exterior angle per vertex.

Polygon Exterior Angles Formula:
The polygon exterior angles formula states that the sum of Polygon Exterior Angles is 360 degrees, irrespective of the type of the polygon. In other words, we can say that the sum of all the exterior angles of a polygon is equal to one full revolution.

Sum of one exterior angle of all vertex of any polygon = 360 degrees.

In case of a regular polygon, the formula to find any exterior angle is obtained by dividing the sum of the exterior angles i.e. 360 by the number of angles, say “n”.

The value of an angle of a regular polygon = 360/n

Here are few examples of Hexagon:

Example 1:
Hexagon has 6 sides. Therefore every exterior angle in hexagon = 360/6 = 60 degrees.

Example 2:
The value of an angle of a regular polygon is 30 degrees. How many sides are there in the polygon?
360/n = 30 which can be rewritten as 360 = 30n.
Thus, n is given by dividing 360 by 30 which results in 12.

Exterior Angles Triangle
In case of triangle, exterior angle lies in between one side of the given triangle and the extension of the other side of the same triangle. Exterior Angles of Triangle can be obtained by adding the measures of the two of the non-adjacent interior angles.

Math Homework Help

As many parents will know, math homework is something kids avoid like the plague. Math may not be everyone's favorite subject but there is no denying it's importance in day to day life. Math skills are necessary and students who take an interest in the subject early on, will have a much easier time studying it in high school.

Much of the lack of interest in math boils down to the way it is delivered in class. To ensure that every student understands what is being taught, teachers need to employ different techniques to explain the concepts. This does not happen very often and students vary between having a vague idea and being completely clueless. When they have to finish their homework, in most cases students simply don't know enough to do their work. Some parents help out but in many households parents are either too pressed for time or not well-versed enough in math themselves to help their kids.

Getting help with math is the best solutions for students and parents who find themselves in this situation. Math tutoring has become very popular over the past decade with several students signing up for them, starting as early as elementary school. Math tutors wok with students on an individual basis, giving them ample time to learn at their own pace and clear every single doubt. Hundreds of students in schools across the country use math tutoring and as a result, have aced their tests and exams, getting As and Bs where they were previously failing.

Many math helpers feature help with math homework as a regular part of their services that students can make use of everyday. Unlike online calculators and programs which calculate the answer for the questions students input, getting professional help ensures that students really learn the concept or theory and how to put it into practice. Students can also practice with math tutors which allows them to really explore the topic as there is someone who can correct them, if need be. Homework help has helped students keep up with their schedules and submit assignments on time, all the while learning more about the topic.

All about acute angles

A very common question for a 5th grader who has just started to learn geometry would be: what is an acute angle? Or What is a acute angle? (Considering that they are not really sure what article to use before the word ‘acute’). Let us now describe an acute angle in simple terms.

A acute angle:
Look at the hands of a clock on your bedroom wall when the time is say 2:00 pm. The hour and the minute hand of the clock make an angle with each other at the centre of the clock. That angle would be an acute angle. From 12:00 noon to 3:00 pm, the angles made by the hands of the clock are acute angles. At 3:00 pm the hands of the clock are at right angles to each other. After 3:00 pm the angle between the hands of the clock are obtuse angles.

If you have a pine tree around your home, look at the top of the tree. The angle made by the two lines in the form of an inverted V at the top is an acute angle.

Acute angle definition:
An angle whose measure is more than 0 degrees and less than 90 degrees is called an acute angle. If the angle measure is in radians, then the angle whose measure is more than 0 radians and less than pi/2 radians is called an acute angle.
Mathematically it is written like this:
If angle A is such that measure of angle A = m0 < = (mIn geometry an acute angle can be generally sketched as follows:

Acute angles in geometry:

An equilateral triangle has all three angles as acute angles. Each of the angles in an equilateral triangle is 60 degrees or pi/3 radians. See picture below:


In a right triangle, one of the angles is 90 degrees (or pi/2 radians), but the other two angles are acute angles. For example see the picture below:

The angle subtended by the chord of a circle at any point in the major segment of the circle would always be a right angle, except if the chord is a diameter of the circle. In such a case, the angle subtended would be a right angle. See the following figure to understand that better:

In the above figure, BC is the chord of a circle and the angle subtended by BC at A = α. Α would be an acute angle.

Basics about Circles

Definition: A circle is a collection of all points in a plane which are at a constant distance (radius) from a fixed point (centre). Properties of a circle encompass use of terms such as chord, segment, sector, diameter etc of a circle. Now let us try to understand some other terms related to properties of circles.

Properties of circle:
A straight line that intersects a circle in two distinct points is called a secant to that circle. In the picture below, we have a circle with centre at C. A line l intersects this circle in two points, A and B. This line is a secant to the circle.

A straight line that intersects (or touches) a circle in just one point is called a tangent to the circle at that point. For a circle at a given point, there can be only one tangent. The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide. See picture below.

Circle theorems:

1. The tangent at any point of a circle is perpendicular to the radius through the point of contact. This we can see in the above picture. The tangent is perpendicular to the radius that joins the point of contact with the centre of the circle.

2. The lengths of tangents drawn from an external point to a circle are equal.

Circle formulas geometry:

Area of a circle: Area of a circle is given by the formula:
A = pi r^2
Area of semi circle: Area of a semi circle of radius r is given by the formula:
A = (pi/2)r^2

Segment of a circle:

The portion (or part) of the circular region enclosed between a chord and the corresponding arc of the circle is called a segment of the circle.

In the picture above, the orange portion is called the minor segment of the circle and the yellow portion is the major segment of the circle. The minor segment corresponds to minor arc and the major segment corresponds to the major arc of a circle.

Area of a segment of a circle is found using the formula below:

Where, theta is the angle subtended by the chord at the centre of the circle and r is the radius of the circle.

Calculate Time - Fourth Grade Math

In grade four, new concepts are introduced in math. Some new concepts are time, multiples and factors, addition and subtraction of three digit numbers, unitary method, measures of length, mass and capacity, fractional numbers, addition and subtraction of fractions, decimals, addition and subtraction of decimals, Introduction to angles.

Introduction to grade four math:

In grade four, the topic time contains the following sub units.

- Measurement of time

-Calender

- Time in second

- Addition and subtraction of time

In this article let us learn about 24-hour clock time.

In the present day world business houses, airlines, railways are busy round the clock. Hence it is convenient to use 24 - hour time representation instead of a.m. and p.m.

1. 12 O' clock midnight is expressed as 00 00 or 24 00

2. 12 O' clock is expressed as 12 00

3. The time between 12 O' clock noon and 12 O' clock midnight is expressed by adding 12 hours to the given hours period.

For example:

25 minutes past 6 in the evening is expressed as 18 25

45 minutes past 11 midnight is written as 23 45

Rules for Writing 24-hour Clock Time:

A day begins at 12 midnight (00:00 hours) and hence at 12 midnight the following day.

Thus 1 day = 24 hours

Rule 1: For any time in a.m. we simply put down the time by writing hours and minutes in two digits numbers.

Rule 2: For any time written in p.m. we simply add 12 hours to the number of hours period and write minutes without separating them.

6:25 a.m is written as 06 25 hours

10:45 a.m is written as 10 45 hours

3:10 p.m. is written as 15 10 hours (3 + 12 = 15)

10:50 p.m. is written as 22 50 hours (10 + 12 = 22)

Example Problems on Grade Fourth Math:

Ex 1: Express 11:25 p.m. in the 24 hours system.

Sol:

Step 1: See which rule can be used.

Step 2: Since the time given is in p.m., add 12 to 11

Step 3: So, 11:25 p.m. = (11 + 12 hours) : 25 min

= 23 25 hours

Ex 2: Express 18 30 hours in terms of a.m. or p.m.

Sol:

18 30 hours means (12 + 6 hours) 30 minutes

= 6:30 p.m.

Ex 3: Express 07:45 p.m. in the 24 hours system.

Sol:

Step 1: See which rule can be used.

Step 2: Since the time given is in p.m., add 12 to 7

Step 3: So, 07:45 p.m. = (7 + 12 hours) : 45 min

= 19 : 45 hours