Two angles are a linear pair. One angle is 8 times as large as the other. What is the measure of each of the angles
8x + x=180 deg
solve for x, then 8x
two angle in a certaun linear pair one angle measures twice as much as the other what is the measure of each angle
To solve this problem, let's first define what a linear pair is. A linear pair consists of two adjacent angles that together form a straight line, which means their sum is always equal to 180 degrees.
Let's assume that one angle in the linear pair is x degrees.
According to the problem, the other angle is 8 times as large as the first angle. So, the measure of the second angle can be represented as 8x degrees.
Since the sum of the angles in a linear pair is always 180 degrees, we can set up the following equation:
x + 8x = 180
Combining like terms, we have:
9x = 180
Dividing both sides of the equation by 9, we find:
x = 20
Now, we can substitute the value of x back into one of the angle measures to find the measure of each angle:
First angle = x = 20 degrees
Second angle = 8x = 8 * 20 = 160 degrees
Therefore, the measure of the first angle is 20 degrees, and the measure of the second angle is 160 degrees.