If the angles of triangle MNO are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
Practice Questions
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Q1
If the angles of triangle MNO are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
40 degrees
60 degrees
80 degrees
90 degrees
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Thus, 9x = 180 degrees, x = 20 degrees. The largest angle = 4x = 80 degrees.
Questions & Step-by-step Solutions
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Q
Q: If the angles of triangle MNO are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
Solution: Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Thus, 9x = 180 degrees, x = 20 degrees. The largest angle = 4x = 80 degrees.
Steps: 9
Step 1: Understand that the angles of triangle MNO are in the ratio 2:3:4.
Step 2: Let the angles be represented as 2x, 3x, and 4x, where x is a common multiplier.
Step 3: Add the angles together: 2x + 3x + 4x.
Step 4: Simplify the equation: 2x + 3x + 4x = 9x.
Step 5: Set the sum of the angles equal to 180 degrees (the total degrees in a triangle): 9x = 180.
Step 6: Solve for x by dividing both sides by 9: x = 180 / 9.
Step 7: Calculate x: x = 20 degrees.
Step 8: Find the largest angle by calculating 4x: 4x = 4 * 20 degrees.
Step 9: Calculate the largest angle: 4x = 80 degrees.
