Question

Two angles form a linear pair. The measure of one angle is 1 and 1/2 times the measure of the other angle. Find the measure of each angle.

Answer 1

To find the measure of each angle in a linear pair where one angle is 1 and 1/2 times the other, set up an algebraic equation representing their sum as 180 degrees. Solve for the smaller angle, then calculate the larger angle.

Step-by-step explanation:

When two angles form a linear pair, they are adjacent (share a common side) and add up to 180 degrees. Given that one angle is 1 and 1/2 times the measure of the other angle, we can use algebra to find the measure of each angle.

Step-by-Step Solution:

1. Let the measure of the smaller angle be x degrees.
2. Since one angle is 1 and 1/2 times the other, the larger angle will be 1.5x degrees.
3. The sum of the angles in a linear pair is 180 degrees, so the equation to solve is x + 1.5x = 180.
4. Combining like terms gives us 2.5x = 180.
5. Dividing both sides by 2.5 gives x = 72 degrees.
6. Therefore, the larger angle is 1.5 × 72 = 108 degrees.

The measures of the two angles are 72 degrees and 108 degrees.

Answer 2

Step-by-step explanation: If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar.