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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 largest 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 largest angle is 2x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (2x - 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 largest 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 largest angle, what is the measure of the smallest angle?
  • Step 1: Let's define the smallest angle as x.
  • Step 2: According to the problem, the second angle is twice the smallest angle, so we write it as 2x.
  • Step 3: The largest angle is 30 degrees less than the second angle, so we write it as 2x - 30.
  • Step 4: In a triangle, the sum of all angles is always 180 degrees. We can write the equation: x + 2x + (2x - 30) = 180.
  • Step 5: Combine like terms in the equation: x + 2x + 2x - 30 = 180 becomes 5x - 30 = 180.
  • Step 6: Add 30 to both sides of the equation: 5x = 210.
  • Step 7: Divide both sides by 5 to find x: x = 42 degrees.
  • Step 8: Since we defined x as the smallest angle, the smallest angle is 42 degrees.
  • Angle Relationships in Triangles – Understanding how the angles in a triangle relate to each other and the properties of triangle angle sums.
  • Algebraic Manipulation – Applying algebra to set up and solve equations based on the relationships between the angles.
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