An angle is made up of two rays that share a common vertex.
The angle ∠XYZ above has two arms: ray YX and ray YZ.
Its vertex is point Y.
Adjacent angles are two angles that share a common vertex and a common arm. They share no interior points.
The word "adjacent" means side-by-side, or directly next to.
This means that adjacent angles are side-by-side angles.
Look at the two angles below.
The first angle is ∠ABC.
What is its vertex?
Yes, it's point B.
The second angle is ∠CBD.
What is its vertex?
Correct. It's point B as well.
The two angles have the same vertex, point B.
Adjacent angles also share a common side.
The two angles below share a common side, ray BC.
Adjacent angles do not share any interior points.
All the points within ∠ABC are on one side.
The points within ∠CBD are on the other side.
None of the points overlap.
This means these two angles are adjacent. ✅
Do these angles have a common vertex?
No, they don't.
Do they have a common side?
No, they don't.
They're not adjacent.
Let's look at these adjacent angles.
When we put ∠ABC and ∠CBD together, they create the bigger angle ∠ABD.
Since the two smaller angles are adjacent, we can add up their measurements to get the measurement of the bigger angle.
∠ABC + ∠CBD = ∠ABD
Let's take a look at the measurements of the two angles:
What is the size of the new, bigger angle ∠ABD?
140° + 40° = 180°
Yes it's 180°. ✅
Tip:
A straight angle measures exactly 180°.
What is the value of n below?
We know the sum of the angles is 75°.
One angle is 25°.
How do we find n?
We subtract the size of the angle we know from the total.
n = total - known angle
Let's subtract:
n = 75° - 25°
n = 50°
The size of the unknown angle is 50°. ✅
Let's check by adding the angles:
50° + 25° = 75°
Fantastic. Our answer is correct.
Great job learning about adjacent angles.
Adjacent angles share a common vertex and side, but no interior points.
Do you think you can spot adjacent angles on your own?
Try the practice to see.