The measures of two angles which form a linear pair are in the ratio 2:7. Find
the measures.
2x+7x = 180
find x, then the angles
56
To find the measures of the two angles that form a linear pair, we need to understand what a linear pair is.
A linear pair of angles is formed when two adjacent angles are formed by two intersecting lines. These two angles will always add up to 180 degrees.
Let's assume that the smaller angle in the ratio is 2x, and the larger angle is 7x.
According to the given ratio, 2x:7x, the sum of these angles is equal to 180 degrees.
So we can write the equation as:
2x + 7x = 180
Combining like terms gives:
9x = 180
To solve for x, we divide both sides of the equation by 9:
9x/9 = 180/9
x = 20
Now that we have the value of x, we can substitute it back into the equation to find the measures of the angles:
Small angle = 2x = 2(20) = 40 degrees
Large angle = 7x = 7(20) = 140 degrees
Therefore, the measures of the two angles that form a linear pair are 40 degrees and 140 degrees.