Question

The ratio of the interior angles of a triangle is 1 : 1 : 4. What are the angle measures? Write the angle measures from least to greatest.

Answer 1

30 , 30 , 120 .

Explanation:

Given :

• The ratio of interior angles of a triangle are in ratio of 1:1:4 .

To find :

• The angles from least to greatest .

Solution :

As we know that the angle sum property is 180° , that is the sum of all the interior angles is 180° .

Let us take the given ratio to be 1x:1x:4x .

Sum of these= 1x + 1x + 4x = 6x .

So we can create a equation as ,

==> 6x = 180°

==> x = 180°/6

==> x = 30°

Now we can find the angles as ,

• two smaller angles = 1x = 30° .
• one larger angle = 4x = 4(30°) = 120° .

Hence the angles of the triangle are 30° , 30° and 120° .

Answer 2

The angle measures from least to greatest are 30°, 30° and 120°.

Explanation:

The interior angles of a triangle sum to 180°.

Given the ratio of the interior angles of a triangle is 1 : 1 : 4 then:

x + x + 4x = 180°

Solve the equation for x:

⇒ 6x = 180°

⇒ x = 30°

Therefore, the angle measures are:

• x = 30°
• x = 30°
• 4x = 4 × 30° = 120°

So the angle measures from least to greatest are 30°, 30° and 120°.