The angle in a triangle are in the form x,2x,3x Find the difference between the smallest and the largest angle

Mathematics

ScanSolve AI Answer

Step-by-step solution

4 steps
  1. Set up the equation for the sum of angles in a triangle.

    The sum of the angles in any triangle is 180∘180^\circ. The given angles are xx, 2x2x, and 3x3x.

    x+2x+3x=180∘x + 2x + 3x = 180^\circ
  2. Solve for xx.

    Combine the terms on the left side of the equation.

    6x=180∘6x = 180^\circ

    Divide both sides by 6.

    x=180∘6x = \frac{180^\circ}{6} x=30∘x = 30^\circ
  3. Calculate the measure of each angle.

    Substitute the value of xx back into the expressions for the angles.
    Smallest angle: x=30∘x = 30^\circ
    Middle angle: 2x=2(30∘)=60∘2x = 2(30^\circ) = 60^\circ
    Largest angle: 3x=3(30∘)=90∘3x = 3(30^\circ) = 90^\circ

  4. Find the difference between the smallest and the largest angle.

    Difference = Largest angle - Smallest angle
    Difference = 90∘−30∘90^\circ - 30^\circ
    Difference = 60∘60^\circ

    The final answer is \boxed{\text{60^\circ}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp