If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?
Practice Questions
1 question
Q1
If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?
60 degrees
80 degrees
90 degrees
120 degrees
Let the angles be 2x, 3x, and 4x. The sum of angles in a triangle is 180 degrees. Therefore, 2x + 3x + 4x = 180. Solving gives x = 20, so the largest angle is 4x = 80 degrees.
Questions & Step-by-step Solutions
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Q
Q: If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?
Solution: Let the angles be 2x, 3x, and 4x. The sum of angles in a triangle is 180 degrees. Therefore, 2x + 3x + 4x = 180. Solving gives x = 20, so the largest angle is 4x = 80 degrees.
Steps: 8
Step 1: Understand that the angles of the triangle are in the ratio 2:3:4. This means we can represent the angles as 2x, 3x, and 4x, where x is a common multiplier.
Step 2: Write down the equation for the sum of the angles in a triangle. The sum of the angles in any triangle is always 180 degrees.
Step 3: Set up the equation: 2x + 3x + 4x = 180.
Step 4: Combine the terms on the left side of the equation: (2x + 3x + 4x) = 9x, so the equation becomes 9x = 180.
Step 5: Solve for x by dividing both sides of the equation by 9: x = 180 / 9.
Step 6: Calculate x: x = 20.
Step 7: Now, find the largest angle, which is represented by 4x. Multiply 4 by the value of x: 4x = 4 * 20.
Step 8: Calculate 4x: 4x = 80 degrees. This is the measure of the largest angle.
