Two lines intersect so that angle 1 and angle 3 are vertical angles, angle 2 and angle 4 are vertical angles, and angle 1 and angle 2 form a linear pair. how do you slove for x and find the measure of all the angles when
angle 2= x sqaured -3x and angle 4= 6x=10
please help it would mean a lot
<2 = x^2-3x
<4 = 6x+10
<2 = <4, so
x^2-3x = 6x+10
x^2-9x-10 = 0
(x-10)(x+1) = 0
x = 10 or -1
Now you can figure out the angles. Remember that
<1+<2 = <3+<4 = 180
but how do i fin <1 and <3?
Did you find <2?
If so, then read my last line above. <1 and <2 are supplementary.
To solve for x and find the measures of all the angles, let's break it down step by step:
1. Use the given information that angles 1 and 3 are vertical angles, and angles 2 and 4 are vertical angles.
- Vertical angles are formed by two intersecting lines and are congruent, meaning they have the same measure.
- So, we can set up the following equation: angle 1 = angle 3 and angle 2 = angle 4.
2. Use the additional information that angles 1 and 2 form a linear pair.
- A linear pair refers to two adjacent angles that form a straight line, totaling 180 degrees.
- So, we can set up the equation: angle 1 + angle 2 = 180 degrees.
Now, let's solve for x and find the measures of all the angles:
Step 1: Set up the equation for angles 1 and 3.
- angle 1 = angle 3
Step 2: Set up the equation for angles 2 and 4.
- angle 2 = angle 4
- Substitute the given expressions: x^2 - 3x = 6x + 10
Step 3: Solve for x.
- Combine like terms: x^2 - 9x - 10 = 0
- Factor or use the quadratic formula to solve for x.
Step 4: Find the value of x and substitute it back into the equations to find the measures of angles 1, 2, 3, and 4.
- Once you have the value of x, substitute it into the expressions for angle 2 and angle 4 to find their measures.
- Substitute the value of x into angle 1 to find its measure (because angle 1 and angle 3 are congruent).
- Substitute the value of x into angle 3 to find its measure (because angle 1 and angle 3 are congruent).
By following these steps, you can find the value of x and the measures of all the angles given the equations provided.