Given RS || TU, m∠7 = (3x - 10), and m∠3 = (2x + 5)
what is m∠1
I don´t know how to solve this. There´s a pic but i can´t post it.
Without the picture there is not much hope of help.
To solve this problem, we need to use the properties of parallel lines and the angles formed by them.
Here's what we know:
- RS is parallel to TU (given).
- Angle 7 has a measure of (3x - 10).
- Angle 3 has a measure of (2x + 5).
We need to find the measure of Angle 1.
To solve for Angle 1, we can use the fact that when two parallel lines are cut by a transversal line, the corresponding angles are congruent.
In this case, Angle 1 and Angle 7 are corresponding angles since they are on the same side of the transversal TU. Therefore, Angle 1 has the same measure as Angle 7.
So, we can set up an equation to solve for x:
(3x - 10) = (2x + 5)
Now, let's solve this equation step by step:
3x - 10 = 2x + 5
3x - 2x = 5 + 10
x = 15
Now that we have the value for x, we can substitute it back into the expression for Angle 7:
m∠7 = (3x - 10)
m∠7 = (3 * 15 - 10)
m∠7 = (45 - 10)
m∠7 = 35
Since Angle 1 is congruent to Angle 7, we have:
m∠1 = m∠7
m∠1 = 35
Therefore, the measure of Angle 1 is 35 degrees.