Angles on a straight line

Angles on a straight line add up to 180 degree

We can draw multiple angle in the straight line and sum of all the angle would add up to 180 degree.

Let us understand the concept with the help of below cases:

Case 01 – One Angle

Given below is a straight line.
There is one angle AOB in the figure which is equal to 180 degree
Hence \angle AOB\ =\ 180\ degree

Case 02: Two Angles in straight line

In the below figure, the straight line is split into two angles.

Since, straight line = 180 degree
then, the angles on straight line will add up to 180 degree
\angle A\ = 45 degree
\angle B\ = 135 degree

Adding Angle A + Angle B:
⟹ 45 + 135 = 180 degree

Case 03: Three Angles in straight line

In the below figure, the straight line is split into three angles

Since, straight line = 180 degree
then, the angles on straight line will add up to 180 degree
\angle A\ = 50 degree
\angle B\ = 95 degree
\angle C\ = 35 degree

Adding Angle A + Angle B + Angle C;
⟹ 50 + 95 + 35 = 180 degree

I hope the concept is clear.
The point is, no matter how many angles divides the straight line, the addition of all the angles will be 180 degrees.

The above concept can be used to solve problems of missing angle.
If one of the angles in a straight line is missing, you can find the angle measurement with the above property.

Let us solve some problems related to this property

Example 01
Find the angle B in the below figure

Solution
\angle A\ = 77 degree

We know the property of straight line:
\angle A\ + \angle B\ = 180 degree

⟹ 77 + \angle B\ = 180
⟹ \angle B\ = 180 – 77
⟹ \angle B\ = 103

Example 02
Find angle D in below figure

Solution
MN is a straight line
\angle A\ = 50 degree
\angle B\ = 60 degree
\angle C\ = 30 degree
\angle D\ = ?

Using the property of straight line:
\angle A\ + \angle B\ + \angle C\ + \angle D\ = 180 degree

⟹ 50+ 60 + 30 + \angle D\ = 180
⟹ \angle D\ = 180 – 140
⟹ \angle D\ = 40 degree

I hope you have understood the concept of angles in a straight line.
Let us solve some questions related to this concept.

Angles on a Straight Line Problems

(01) Find the value of angle x in the below figure

(a) 65 degree
(b) 54 degree
(c) 60 degree
(d) 64 degree

MN is a straight line
\angle A\ = 126 degree


Using Property of straight line, we know that:
\angle A\ + \angle B\ = 180
126 + \angle B\ = 180
\angle B\ = 180 – 126
\angle B\ = 54 degree

Option (b) is the right answer

(02) Find the value of angle A in below figure

(a) 150 degree
(b) 145 degree
(c) 140 degree
(d) 135 degree

\angle B\ = 45 degree

RK is a straight line
Using Property of straight line:
\angle A\ + \angle B\ = 180
\angle A\ + 45 = 180
\angle A\ = 180 – 45
\angle A\ = 135 degree

Option (d) is the right answer

(03) Find the angle x in the below figure

(a) 72 degree
(b) 80 degree
(c) 70 degree
(d) 85 degree

\angle A\ = 40 degree
\angle B\ = 68 degree
\angle x\ = ?

Using the property of straight line:
\angle A\ + \angle B\ + \angle x\ = 180 degree

⟹ 40 + 68 + \angle x\ = 180
⟹ \angle x\ = 180 – 108
⟹ \angle x\ = 72 degree

Option (a) is the right answer

(04) Find the angle x in below figure

(a) 120 degree
(b) 182 degree
(c) 128 degree
(d) 140 degree

\angle A\ = 20 degree
\angle B\ = 32 degree
\angle x\ = ?

Using the property of straight line:
\angle A\ + \angle B\ + \angle x\ = 180 degree

⟹ 20 + 32 + \angle x\ = 180
⟹ \angle x\ = 180 – 52
⟹ \angle x\ = 128 degree

Option (c) is the right answer

(05) Find the angle x in the below figure

(a) 55 degree
(b) 65 degree
(c) 70 degree
(d) 50 degree