Definition of an Acute Angle

The different types of angle have different types of names. Where the angle is less than 90 radiant is called as acute angle. The acute angle is smaller angle compared with other type of angle such as right angle, obtuse angle, straight angle, reflex angle, and full angle.  The angle which is larger is called as reflex angle.

Definition of a Acute Angle
Definition acute angle, an angle which is less then 90 radiant is called as acute angle. Compared to the other types of angle, an acute angle is very smaller that is in between 0-90 radiant. Also that acute triangle are those where all the interior angle are acute.

Definition of an Acute Angle
An angle of less then 90˚ is called as acute angle and it has three angles. An angle which is exactly 90˚ is a right angle but it is not an acute angle, since it is less than 90˚ or between 0˚-90˚.

Acute Angle Definition Math
An angle which measures less than 90˚ or in between 0˚-90˚ is called as acute angle. In other words, acute angle is a positive angle that measures less than 90˚. Simply it is defined as, an angle of less than 90˚.

Geometry Acute Angle
In geometry, an angle is line segments that intersect in the same plane or it is the amount of bend between two lines. The angles are formed by two intersecting rays at the point of intersection or sharing of same end point. The angles are used to measure the turns in between the two arms. The unit of an angle is degree or radiant. In order to measure an angle from a circle that is a two dimensional plane, if the angle measures greater than 0˚ and less than 90˚ is called as acute angle. The acute angle is referred by the alphabets like ABC or DEF.

In above figure angle A is acute which measures greater than 0˚ and less than 90˚. It is formed by the intersection of two rays like AB and AC, which are called as sides of angle or arms. Where the angle is formed is called as vertex. In figure, the angle 1 which is, marked by square sign is called acute angle. Acute angle is smaller than right angle which is exactly equal to 90˚. Similarly the angle 2 is complementary of an angle 1. Complementary angle of an acute angle is also acute as it measures greater than 0˚ and less than 90˚.

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

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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.