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?
Practice Questions
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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?
30 degrees
45 degrees
60 degrees
75 degrees
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.
Questions & Step-by-step Solutions
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Q
Q: 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?
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.
Steps: 8
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.
