angle d and e for linear pair and measure of angle e equal 3m angle d find the measure of each angle and the measure of the complement of angle d
Review you notes for the definition of linear pair. It means that d+e = 180°
d + 3d = 180
d = 45
e = 135
So, since complementary angles add to 90°, what's d's complement?
To find the measures of angle D and E, let's start by understanding what a linear pair of angles is. A linear pair consists of two adjacent angles formed by two intersecting lines. The sum of the angles in a linear pair is always 180 degrees.
Let's denote the measure of angle D as "x". According to the given information, the measure of angle E is 3 times the measure of angle D. So, the measure of angle E is 3x.
Since angle D and angle E form a linear pair, their sum is 180 degrees:
x + 3x = 180
Now, let's solve for x:
4x = 180
x = 180/4
x = 45
Therefore, the measure of angle D (x) is 45 degrees.
To find the measure of angle E, we substitute the value of x into 3x:
3(45) = 135
Hence, the measure of angle E is 135 degrees.
To find the complement of angle D, we need to remember that the sum of an angle and its complement is always 90 degrees. So:
Angle D + Complement of D = 90
Substituting the measure of angle D (45), we have:
45 + Complement of D = 90
Now, let's solve for the Complement of D:
Complement of D = 90 - 45
Complement of D = 45
Therefore, the measure of the complement of angle D is 45 degrees.