Triangles Contain 180 Degrees

Find the Missing Angle "C"

Answer explanation

Start With:   A + B + C = 180°
     
Fill in what we know:   66° + 39° + C = 180°
     
Rearrange:   C = 180° - 66° - 39°
     
Calculate:   C = 75°

Find the Missing Angle "C"

Answer explanation

Start With:   A + B + C = 180°
Fill in what we know:   56.7° + 41.2° + C = 180°
Rearrange:   C = 180° − 56.7° − 41.2° = 180° − 97.9°
Calculate:   C = 82.1°

What is the size of the missing angle "C"?

Answer explanation

The triangle has two equal sides of length 4 units, so it is isosceles.

So the angle marked B must also be 39°

Next, in a triangle all three angles must add to 180°

So:   A + B + C = 180°
     
Fill in what we know:   39° + 39° + C = 180°
     
Rearrange   C = 180° - 39° - 39°
     
Calculate:   C = 102°

What is the size of the missing angle "B"?

Answer explanation

The triangle has two equal sides of length 10 units, so it is isosceles.
So the two angles marked B must be equal.

Next, in a triangle all three angles must add to 180°
So:   103.6° + B + B = 180°
Then: 103.6° + 2B  = 180°

Rearrange:   2B = 180° − 103.6° = 76.4°

Divide by 2:   B = 76.4° ÷ 2 = 38.2°

A triangle has angles in the ratio 2 : 3 : 4
What is the size of the smallest of the three angles?

Answer explanation

2 + 3 + 4 = 9
So we have to divide 180° into 9 equal parts:
180° ÷ 9 = 20°

The smallest angle is 2 parts = 2 × 20° = 40°

A triangle has angles in the ratio 4 : 5 : 6
What is the size of the largest of the three angles?

Answer explanation

4 + 5 + 6 = 15
So we have to divide 180° into 15 equal parts:
180° ÷ 15 = 12°

The largest angle is 6 parts = 6 × 12° = 72°

 

What is the size of angle ACD?

Answer explanation

In triangle ABC:

Start with:   A + B + C = 180°
     
Fill in what we know:   75° + 61° + C = 180°
     
Rearrange:   C = 180° − 75° −  61°
                      = 180° −  136°
Calculate:   C = 44°

Now use angles on a straight line add to 180° to find angle ACD
ACD = 180° −  44° = 136°

Can you see a quicker way to do this?
Since we subtracted 136° from 180° to get 44° and then subtracted 44° from 180° to get 136°, we could just give the answer as 75° + 61° = 136°

ABDC is a quadrilateral.
What is the angle ACD?

Answer explanation

First use angles of a triangle add to 180°, in triangle ABC:

58° + 74° + C = 180°
⇒ C = 180° − 58° − 74° = 180° − 132° = 48°

Next use angles of a triangle add to 180°, in triangle BDC:
Since one angle is 90° and the triangle is isosceles, the other two angles must both be 45°

So we have:


So angle ACD = 48° + 45° = 93°

Triangle ABC is right angled and AD = BD = CD
What is the size of angle ADB?

Answer explanation

Triangles ABD and BCD are isosceles and therefore have two equal angles.
And the angles in each triangle must add to 180°

The following diagram shows all of the angles:


So Angle ADB = 80°

Angle BAC = 30°, angle CBA = 25° and sides AC = AD

What is the size of angle BCD?

Answer explanation

Triangle ABC has two known angles: 25° and 30°
And the angles in a triangle must add to 180°
So the third angle (ACB) must be 180° - 25° - 30° = 125°

Triangle ACD has two equal sides (an isosceles triangle) and so has two equal angles.
And the angles in a triangle must add to 180°
So the other two angles must both be: (180°-30°)/2 = 75°

So Angle BCD must be 125° - 75° = 50°

The following diagram shows all of the angles: