If m( angle 1) = 4x + 10 and m( angle 7) = 6x + 4, what are the measures of angles 1 and 7?
I'm not sure how to show my work. Angle 1 and angle 7 are congruent alternate exterior angles
Well, let's start by equating the measures of the angles:
4x + 10 = 6x + 4
Now, let's solve for x:
4x - 6x = 4 - 10
-2x = -6
x = -6 / -2
x = 3
Now that we have the value of x, let's substitute it back into the equations to find the measures of the angles:
m(angle 1) = 4(3) + 10
m(angle 1) = 12 + 10
m(angle 1) = 22
m(angle 7) = 6(3) + 4
m(angle 7) = 18 + 4
m(angle 7) = 22
Therefore, angle 1 has a measure of 22 degrees and angle 7 also has a measure of 22 degrees.
To find the measures of angles 1 and 7, we can set their corresponding expressions equal to each other because they are congruent.
Therefore, we have:
4x + 10 = 6x + 4
To solve this equation for x, we need to isolate it on one side of the equation. We can do this by subtracting 4x from both sides and subtracting 4 from both sides:
4x - 4x + 10 - 4 = 6x - 4x + 4 - 4
10 = 2x
To isolate x, divide both sides of the equation by 2:
10/2 = 2x/2
5 = x
Now that we have found the value of x, we can substitute it back into either equation to find the measures of angles 1 and 7.
Let's use the equation m(angle 1) = 4x + 10:
m(angle 1) = 4(5) + 10
m(angle 1) = 20 + 10
m(angle 1) = 30
Therefore, the measure of angle 1 is 30 degrees.
Since angles 1 and 7 are congruent, the measure of angle 7 is also 30 degrees.
To find the measures of angles 1 and 7, we need to set up an equation as they are congruent alternate exterior angles.
Given that m(angle 1) = 4x + 10 and m(angle 7) = 6x + 4, we can set up an equation as follows:
4x + 10 = 6x + 4
Now, we can solve this equation to find the value of x. Subtract 4x from both sides:
10 = 2x + 4
Subtract 4 from both sides:
6 = 2x
Divide by 2:
3 = x
Now that we know the value of x, we can substitute it back into the expressions for m(angle 1) and m(angle 7) to find their respective measures.
m(angle 1) = 4x + 10 = 4(3) + 10 = 12 + 10 = 22
m(angle 7) = 6x + 4 = 6(3) + 4 = 18 + 4 = 22
Therefore, the measures of angles 1 and 7 are both 22 degrees.
If they are "congruent" then they must be equal
so solve
6x+4 = 4x + 10 for x, then sub it back into the angle expressions