To parallel lines l and m are cut by transversal t if the interior angles of the same side of t be (2x-8) and (3x-7) find the measure of each of these angles
the angles are supplementary (sum to 180º)
2x - 8 + 3x - 7 = 180
m∠3=78
To find the measure of each angle, we can set them equal to each other and solve for x.
Given:
Interior angles of the same side of transversal t: (2x-8) and (3x-7)
Setting them equal to each other:
2x-8 = 3x-7
Now, let's solve for x:
2x-3x = -7+8
-x = 1
Divide both sides by -1 to solve for x:
x = -1
Now, substitute the value of x back into the equations to find the measures of the angles:
Angle 1: 2x-8 = 2(-1)-8 = -2-8 = -10 degrees
Angle 2: 3x-7 = 3(-1)-7 = -3-7 = -10 degrees
Therefore, the measure of each angle is -10 degrees.
To find the measure of each of these angles, we can set up an equation based on the given information.
We know that the interior angles of the same side of the transversal will add up to 180 degrees (since the lines are parallel). Therefore, we can write the equation:
(2x - 8) + (3x - 7) = 180
Now, let's solve this equation to find the value of x.
Combine like terms:
5x - 15 = 180
Add 15 to both sides:
5x = 195
Divide both sides by 5:
x = 39
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measures.
Angle 1:
2x - 8 = 2(39) - 8 = 78 - 8 = 70 degrees
Angle 2:
3x - 7 = 3(39) - 7 = 117 - 7 = 110 degrees
Therefore, the measures of the angles are 70 degrees and 110 degrees.