Two angles form a linear pair.The measure of one angle is 24 more than the measure of the other angle.Find the measure of the each angle
a + b = 180
a - b = 24
---------------------- subtract
0 + 2 b = 156
b = 78
then a = b+24 = 102
======================
check
102 - 24 = 78 yes
78 + 102 = 180 yes
To solve this problem, let's set up an equation:
Let the measure of one angle be x.
The measure of the other angle would then be (x + 24), since it is 24 more than the first angle.
According to the problem, these two angles form a linear pair, which means they add up to 180 degrees.
So, the equation can be written as:
x + (x + 24) = 180
Simplifying the equation:
2x + 24 = 180
2x = 180 - 24
2x = 156
x = 156/2
x = 78
Therefore, the measure of one angle is 78 degrees, and the measure of the other angle is (78 + 24) = 102 degrees.