A smaller angle of 45°, a larger angle of 135°, and a straight line formed.
Here's how to find the measure of each angle in a linear pair with one angle being 1/3 the measure of the other:
1. Linear Pair: When two lines intersect at a point, they form a straight angle of 180 degrees. Two angles that share a vertex and together form a straight line are called a linear pair.
2. Sum of Angles: Since a linear pair forms a straight line, the sum of their measures must be 180 degrees.
3. Ratio of Measures: We know one angle's measure is 1/3 the measure of the other angle. Let x be the measure of the smaller angle. Then, the larger angle would be 3x.
4. Equation: Set up an equation based on the sum of angles and the ratio of their measures: x + 3x = 180 degrees.
5. Solve for x: Combine like terms: 4x = 180 degrees. Divide both sides by 4 to find x: x = 45 degrees.
6. Find Measures: Now that you know the smaller angle is 45 degrees, the larger angle is 3x = 3 * 45 degrees = 135 degrees.
Therefore, the smaller angle in the linear pair measures 45 degrees and the larger angle measures 135 degrees.
Question:
Two angles form a linear pair. The measure of one angle is 1/3 the measure of the other angle. Find the measure of each angle.