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In a triangle, if one angle is twice the size of another angle, and the third an

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Question: In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the first angle, what is the measure of the smallest angle?

Options:

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Correct Answer: 30 degrees

Solution: 

Let the smallest angle be x. Then the second angle is 2x and the third angle is x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (x - 30) = 180. Solving this gives x = 30 degrees.

In a triangle, if one angle is twice the size of another angle, and the third an

Practice Questions

Q1
In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the first angle, what is the measure of the smallest angle?
  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Questions & Step-by-Step Solutions

In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the first angle, what is the measure of the smallest angle?
  • Step 1: Let's define the smallest angle as 'x'.
  • Step 2: The second angle is twice the smallest angle, so it is '2x'.
  • Step 3: The third angle is 30 degrees less than the first angle, so it is 'x - 30'.
  • Step 4: In a triangle, the sum of all angles is 180 degrees. So we can write the equation: x + 2x + (x - 30) = 180.
  • Step 5: Combine like terms in the equation: 4x - 30 = 180.
  • Step 6: Add 30 to both sides of the equation: 4x = 210.
  • Step 7: Divide both sides by 4 to find 'x': x = 210 / 4.
  • Step 8: Calculate the value: x = 52.5 degrees.
  • Step 9: Since we need the smallest angle, we check if x is the smallest angle. The angles are x = 52.5, 2x = 105, and x - 30 = 22.5.
  • Step 10: The smallest angle is 22.5 degrees.
  • Angle Relationships in Triangles – Understanding how the angles in a triangle relate to each other and the property that their sum equals 180 degrees.
  • Algebraic Manipulation – Using algebra to set up equations based on relationships between angles and solving for unknowns.
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