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A carpenter designed the top of a table in a triangular shape as shown below. Determine the difference between the largest and the smallest angles in the figure above.

Mathematics

ScanSolve AI Answer

Answer

90∘90^\circ

Step-by-step solution

4 steps
  1. The sum of angles in a triangle is 180∘180^\circ.

    Set up an equation with the given angles.

    (n−30∘)+n∘+(2n+10∘)=180∘(n - 30^\circ) + n^\circ + (2n + 10^\circ) = 180^\circ
  2. Solve the equation for nn.

    n−30+n+2n+10=180n - 30 + n + 2n + 10 = 180 4n−20=1804n - 20 = 180 4n=180+204n = 180 + 20 4n=2004n = 200 n=2004n = \frac{200}{4} n=50n = 50
  3. Substitute the value of nn back into the expressions for each angle to find their measures.

    First angle: n−30∘=50∘−30∘=20∘n - 30^\circ = 50^\circ - 30^\circ = 20^\circ
    Second angle: n∘=50∘n^\circ = 50^\circ
    Third angle: 2n+10∘=2(50∘)+10∘=100∘+10∘=110∘2n + 10^\circ = 2(50^\circ) + 10^\circ = 100^\circ + 10^\circ = 110^\circ

  4. Identify the largest and smallest angles and calculate their difference.

    The angles are 20∘20^\circ, 50∘50^\circ, and 110∘110^\circ.
    Largest angle = 110∘110^\circ
    Smallest angle = 20∘20^\circ
    Difference = Largest angle - Smallest angle
    Difference = 110∘−20∘=90∘110^\circ - 20^\circ = 90^\circ

    The difference between the largest and the smallest angles is 90∘\boxed{90^\circ}.

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