The angles that form a linear pair are in The ratio 2:7.find the measure of each angle.
2x+7x = 180
x=20
so ...
To find the measure of each angle in a linear pair, we need to understand what a linear pair is.
A linear pair is formed by two adjacent angles that are formed when two lines intersect. The measure of a straight line is 180 degrees, and a linear pair of angles always adds up to 180 degrees.
Let's assume the measure of the smaller angle in the linear pair is 2x, and the measure of the larger angle is 7x. Since the measure of the angles are in the ratio 2:7, these values represent the ratio of the measures of the angles.
According to the property of a linear pair, the sum of these two angles must equal 180 degrees.
So, we can set up an equation: 2x + 7x = 180.
Combining like terms: 9x = 180.
Dividing both sides by 9: x = 20.
Now, substitute x back into the equations for the measures of the angles:
The measure of the smaller angle = 2x = 2(20) = 40 degrees.
The measure of the larger angle = 7x = 7(20) = 140 degrees.
Therefore, the measure of each angle in the linear pair is 40 degrees and 140 degrees.