# Triangles

# How to Find the Missing Angle

## Triangles - Find the Missing Side Angle - How it Works - Video

### Example 1

Example 1:

Triangles have 3 angles and the sum of those 3 angles is always 180°. Now if we combine all the angles, they form half a circle, which is 180°. Also, when we combine the angles, a straight line (red line) is formed which is also 180°.

Now we need to add the orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) to find the missing angle. So we have ==> 68° + x + 48° = 180°.

Next we add ==> 68° + 48° = 116°. Now we can write the equation as x + 116° = 180° then x = 64° after we subtracted the term 116° on both sides.

So our final result is x = 64°.

### Example 2

Example 2:

Triangles have 3 angles and the sum of those 3 angles is always 180°. Now if we combine all the angles, they form half a circle, which is 180°. Also, when we combine the angles, a straight line (red line) is formed which is also 180°. In this case we have an isosceles triangle, so the orange angle (<CAB) and the yellow angle (BCA) are the same, 65°.

Now we need to add the orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) to find the missing angle. So we have ==> 65° + x + 65° = 180°.

Then we add ==> 65° + 65° = 130°. Now we can write the equation as x + 130° = 180° then x = 50° after we subtracted the term 130° on both sides.

So our final result is x = 50°.

### Example 3

Example 3:

Triangles have 3 angles and the sum of those 3 angles is always 180°. Now if we combine all the angles, they form half a circle, which is 180°. Also, when we combine the angles, a straight line (red line) is formed which is also 180°. In this case we have an equilateral triangle, so each angle is the same, 60°.

Now we need to add the orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) to show that they are all the same. Now, we have ==> 60° + 60° + 60° = 180°

Then we add ==> 60° + 60° = 120°. Now we can write the equation as 120° + 60° = 180°.

Now we add ==> 120° + 60° = 180°. Now we can write the equation as 180° = 180°.

So our final result is x = 60°.

### Example 4

Example 4:

Triangles have 3 angles and the sum of those 3 angles is always 180°. Now if we combine all the angles, they form half a circle, which is 180°. Also, when we combine the angles, a straight line (red line) is formed which is also 180°. In this case we have an isosceles triangle, so the orange angle (<CAB) and the yellow angle (BCA) are the same.

Now we need to add the orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) to find the missing angle. So we have ==> <CAB + 82° + <BCA = 180°.

Now we must subtract 82° on both sides ==> <CAB + <BCA = 98°. Now we divide 98° by 2 = 49° since both angles are the same.

So our final result is x = 49°.

### Example 5

Example 5:

Triangles have 3 angles and the sum of those 3 angles is always 180°. Now if we combine all the angles, they form half a circle, which is 180°. Also, when we combine the angles, a straight line (red line) is formed which is also 180°. In this case we have an right triangle (orange angle), 90°.

Now we need to add the orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) to find the missing angle.

Now, we have 90° + 18° + x = 180°.

Next, we add ==> 90° + 18° = 108°. Now we can write the equation as 108° + x = 180°.

Then we subtract 72° on both sides ==> x = 72°.

So our final result is x = 72°.

## Live Worksheet

Here is the link if you prefer.