for paralleogram ABCD, m<1=x+25 and m<2=2x find m<2
what and where are m<1 and m<2 etc?
The two angles are Alternate Interior angles
To find the measure of angle 2 (m<2), we need to consider the given information about angle 1 (m<1) and use the properties of parallelograms.
In a parallelogram, opposite angles are congruent, which means that angle 1 (m<1) and angle 3 (m<3) are equal in measure.
The sum of the angles in a straight line is 180 degrees, so we can set up an equation using angle 1 and angle 3 as follows:
m<1 + m<3 = 180 degrees
Given that m<1 = x + 25, we substitute this value into the equation:
(x + 25) + m<3 = 180 degrees
To solve for m<2, we need the measure of angle 3 (m<3). Thankfully, we have another piece of information: angle 2 (m<2) is equal to 2x.
Since angle 2 and angle 3 are opposite angles in the parallelogram, they are congruent:
m<2 = m<3
So, we can substitute m<3 with m<2 in the equation:
(x + 25) + m<2 = 180 degrees
Substituting 2x for m<2:
(x + 25) + 2x = 180 degrees
Now we can solve the equation to find the value of x:
3x + 25 = 180 degrees
3x = 155 degrees
x = 155 degrees / 3
x ≈ 51.67 degrees
Now that we know the value of x, we can find the measure of angle 2 (m<2) by substituting it into the expression given for angle 2:
m<2 = 2x
m<2 = 2(51.67)
m<2 ≈ 103.34 degrees
Therefore, the measure of angle 2 (m<2) is approximately 103.34 degrees.