Answer: <em>x</em> = 20
Step-by-step explanation:
If line <em>m</em> is parallel to line <em>n</em>, the two angles given will be congruent because they will be alternate exterior angles (which are congruent).
This means we will set them equal to each other and solve for <em>x</em>.
Given:
(4<em>x</em> - 23) = (2<em>x</em> + 17)
Add 23 to both sides of the equation:
4<em>x</em> = 2<em>x</em> + 40
Subtract 2<em>x</em> from both sides of the equation:
2<em>x</em> = 40
Divide both sides of the equation by 2:
<em>x</em> = 20
2. Distributive Property
4 is distributed and multiplied inside the parenthesis to x and -5.
4. Subtraction Property of Equality
x is subtracted from both sides of the equation.
4x - x - 22 = x - x + 3
3x - 22 = 3
5. Subtraction Property of Equality
22 is added to both sides of the equation.
3x - 22 + 22 = 3 + 22
3x = 25
6. Division Property of Equality
3 is divided from both sides of the equation.
= 
x =
Answers:
a. Given
b. Transitive property of congruence
c. Vertical angles are congruent
d. Transitive property of congruence
Let me know if you need any clarification as to how I got those answers. They should be self-explanatory but I'm happy to clarify further if needed.
Complementary angles have a sum of 90
32+2x+14=90
2x+46=90
2x=44
x=22 the second angle is 58
2(22)+14=58
We can subtract the sum of the two trinomials by one of the trinomials.
(7x²-5x+4)-(3x²+2x-1)
Let's look at each part.
7x²-3x²=4x²
-5x-2x=-7x
4-(-1)=5
So, the trinomial should look like:
4x²-7x+5
So, C. 4x²-7x+5 is the other trinomial.
