Straight Angle: Measurement, Construction, Properties & Theorems

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Straight angle is an angle with the sides opposite to the vertex in the same straight line that equals two right angles. A straight angle measures 180° (half a revolution, two right angles, or π radians). The angles form a straight line that passes through the vertex. A straight angle is also known as a 'flat angle.'

Table of Content

Straight Angle Measurement
Properties of Straight Angle
Theorems of Straight Angle
Straight Angle Construction
Things to Remember
Sample Questions

Key Takeaways: Straight angle, Angle, Liens, Straight lines, Vertex, Line segments

Also read: Isosceles Triangle Theorems

Straight Angle Measurement

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A straight angle is similar to a straight line and has an angle measurement greater than an obtuse angle. The measurement of 180° creates a straight angle between the two intersecting lines. Straight angles can be formed by connecting three points on any straight line, each of which has a coordinate value. The outside points are the endpoints of two line segments, and the middle point is the vertex where these two lines intersect at an angle of 180°.

Straight Angle

The video below explains this:

Straight Angle Detailed Video Explanation:

Properties of Straight Angles

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Straight angles have the following important properties:

Both sides of a straight angle are perpendicular to each other.
Half of the rotation is completed by the straight angle.
The degree of straightness is 1800.
Straight angles can be created by joining two right angles together.

Also read: Collinear points

Straight Angle Theorems

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According to the straight angle theorem, all straight angles are 180 degrees. A straight angle is formed when the legs of an angle point exactly in opposite directions. A straight angle is denoted by the symbol 180 (in degrees) or (in radians).

In geometry, one good example is a line segment, the endpoints of which extend in the opposite direction.

Construction of Straight Angle

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The steps for making a Straight Angle are as follows:

Using a ruler, draw a straight line OB with an arrowhead at B.

Place the protractor on this line so that the protractor's baseline is adjusted over OB. Point B should be oriented towards the protractor's 0°.

Mark the point starting at 0° and working your way up to 180°. When you reach 180°, make a mark on the paper with the letter A.

Now connect the vertex of the OB line to the marked point A. The arrowhead on the second ray OA should be at A.

Also read: Minors and Cofactors

Things to Remember

Straight angles appear to be straight lines, but they have two arms. A straight line, on the other hand, has only one arm that points in one direction.
When the sum of an acute angle and an obtuse angle is equal to a straight angle, those angles are considered supplementary.
When we look at the angles within a circumference, we can see that they divide the circle into two equal halves and correspond to the circumference's diameter.
It is the boundary between convex (acute, right, and obtuse angles) and concave angles.
When you stretch your arms or a dancer stretches their legs you can see straight angles.

Also read: Properties of Determinants

Sample Questions

Ques: Find the value of angle C in ∠ABC where ∠ A=25°and ∠B=90° (3 marks)

Ans: Given ∠ A=25°and ∠B=90°

We know that,

The sum of interior angles of a triangle is 180°

Thus, ∠A+ ∠B+∠C = 180°

or, 25°+ 90° + ∠C = 180°

Or, ∠C = 180°- 115°

or, ∠C= 65°

Ques: Find the value of angle D in a Quadrilateral ABCD, where∠ A=100°, ∠B=60° and ∠C=35° (3 marks)

Ans: ∠A= 100°

∠B=60°

∠C= 35°

Here, we need to find the value of D

Therefore,

∠ A+∠B+∠C+∠D= 360°

Or, 100°+60°+35°= 360°

Or, 195°+ ∠D = 360°

Or, ∠D= 165°

Ques: ∠AOB is a straight angle, ∠AOC = (3x+20)° and ∠ BOC =(4 x-36)°. Find the value of the x. (3 marks)

Ans: As given that∠ AOC = (3x + 20)° and ∠BOC = (4x- 36) °and AOB is a straight angle.

We know that straight angle measures 180°

Therefore,

∠AOB= ∠AOC +∠BOC

180° = (3x+20)°+ (4x- 36)°

180°= 7x-16

7x= 196°

x= 28°

Ques: Find the angle complementary to the angle 50°. (3 marks)

Ans: The given angle is 50°

Here, we need to find the complementary of it

We know that two angles are complementary when they add up to 90°

Let the complementary angle be x

Now

x= 90°-50°=40°

Ques: find the supplementary of the angle 120° (2 marks)

Ans: The given angle is 120°

Here , we need to find the supplementary of it,

Let supplementary angle be x,

x= 180°-120°=60°

Ques: ∠AOB is a straight angle, ∠AOC = 68°, and ∠BOC= x°. Find the value of the x. (2 marks)

Ans: As given that ∠AOC =68° AND ∠AOB is a straight angle

We know that straight angle measures 180°

Therefore,

180°=68°+x

x=112°

Ques: The difference between the two complementary angles is 180°. Find the measure of the angle. (3 marks)

Ans: Let one angle be of measure x°,

Then complement of x= (90-x)°

difference= 18°

Therefore,(90-x)°-x° =18°

Or, 90°-90°-2x= 18°-90°

Or, x=72/2

x= 36°

Also, 90°-x= 54°

Therefore the two angles are 36° and 54°

Ques: The measure of two supplementary angles are (3x + 15)° and (2x + 5)°. Find the value of x. (3 marks)

Ans: According to the problem (3x-15)° and (2x-5)° are complementary

(3x-15)° + (2x+5)° = 180°

Or, 3x+15+2x+5= 180°

Or, 5x+20°= 180°

Or, 5x= 160/5

x= 32°

Also Read:

Perimeter of a Parallelogram	Area of Parallelogram and Triangles
Parallelogram	Angles of a Parallelogram
Difference Between Rhombus and Parallelogram	Vector Formula
Circle	Semicircle

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1.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals
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2.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.
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5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$
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Straight Angle: Measurement, Construction, Properties & Theorems

Straight Angle Measurement

Straight Angle Detailed Video Explanation:

Properties of Straight Angles

Straight Angle Theorems

Construction of Straight Angle

Things to Remember

Sample Questions

CBSE X Related Questions

1.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

4.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

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Straight Angle: Measurement, Construction, Properties & Theorems

Straight Angle Measurement

Straight Angle Detailed Video Explanation:

Properties of Straight Angles

Straight Angle Theorems

Construction of Straight Angle

Things to Remember

Sample Questions

CBSE X Related Questions

1.If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

4.The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

5.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

4.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.