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Find the Value of x for Angles on a Straight Line (2x° and x°)
Mathematics
Grade 7 (Junior High School)
Question Content
Find the value of x, given that three angles formed on a straight line are 2x°, x°, and the straight angle is split into these two angles along with the implied straight line angle relationship.
Correct Answer
x = 60
Detailed Solution Steps
1
Step 1: Recognize that the sum of angles on a straight line is 180° (a straight angle measures 180°).
2
Step 2: Set up the equation based on the angle relationship: 2x + x = 180.
3
Step 3: Combine like terms: 3x = 180.
4
Step 4: Solve for x by dividing both sides of the equation by 3: x = 180 ÷ 3 = 60.
Knowledge Points Involved
1
Straight Angle
A straight angle is an angle that measures exactly 180°, formed by a straight line. When multiple angles lie on a straight line, their sum equals 180°.
2
Solving One-Variable Linear Equations
A one-variable linear equation is an equation with a single variable raised to the power of 1. To solve it, combine like terms and isolate the variable by performing inverse operations on both sides of the equation.
3
Angle Addition Postulate for Straight Lines
This postulate states that if two or more adjacent angles form a straight line, the sum of their measures is equal to 180°. It is used to set up equations for unknown angle measures in geometric diagrams with straight lines.
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