If the measure of an angle is increased by 20 degrees, and the new angle is thre
Practice Questions
Q1
If the measure of an angle is increased by 20 degrees, and the new angle is three times the original angle, what is the measure of the original angle?
20 degrees
30 degrees
40 degrees
60 degrees
Questions & Step-by-Step Solutions
If the measure of an angle is increased by 20 degrees, and the new angle is three times the original angle, what is the measure of the original angle?
Step 1: Let the original angle be represented by the variable x.
Step 2: According to the problem, if we increase the angle by 20 degrees, we get x + 20.
Step 3: The problem states that this new angle (x + 20) is equal to three times the original angle (3x).
Step 4: We can write the equation: x + 20 = 3x.
Step 5: To solve for x, first subtract x from both sides of the equation: 20 = 3x - x.
Step 6: This simplifies to 20 = 2x.
Step 7: Now, divide both sides by 2 to find x: x = 20 / 2.
Step 8: This gives us x = 10 degrees, which is the original angle.
Step 9: However, the problem states that the new angle is three times the original angle, which means we need to check if 10 degrees satisfies the condition.
Step 10: If the original angle is 10 degrees, then the new angle would be 10 + 20 = 30 degrees.
Step 11: Now check if 30 degrees is three times the original angle: 3 * 10 = 30 degrees, which is correct.
Step 12: Therefore, the measure of the original angle is 10 degrees.
Algebraic Equations – The question tests the ability to set up and solve a linear equation based on a word problem involving angles.
Angle Relationships – Understanding how to manipulate angles and their relationships when one angle is expressed in terms of another.
