ll in the missing information in this Algebraic proof. Please label your answers as a, b, c, ...
Two lines intersect. Angle 1 equals left parentheses 3 times x + 20 right parentheses. Angle 2 = left parentheses 5 times x - 16 right parentheses, Angles 1 and 3 are vertical angles.
The measure of angle 1 = the measure of angle 3. (Vertical Angles are Congruent)
a.) _____ = (5x - 16) (Substitution)
b.) -2x + 20 = _____ (Subtraction Prop. of Equality)
c.) -2x = _____ (Subtraction Prop. of Equality)
d.) x = _____ (Division Prop. of Equality (4 points)
a.) Angle 1 = 3x + 20 (Substitution, since Angle 1 is equal to 3 times x + 20 according to the given information).
b.) -2x + 20 = 5x - 16 (Substitution, substituting Angle 1 with 3x + 20 and Angle 2 with 5x - 16 as stated in the question).
c.) -2x + 20 - 20 = 5x - 16 - 20 (Subtraction Property of Equality, subtracting 20 from both sides of the equation).
Simplifying further, we get:
-2x = 5x - 36
d.) -2x - 5x = 5x - 36 - 5x (Subtraction Property of Equality, subtracting 5x from both sides of the equation).
Simplifying further, we get:
-7x = -36
e.) -7x/-7 = -36/-7 (Division Property of Equality, dividing both sides of the equation by -7).
Simplifying further, we get:
x = 36/7
To fill in the missing information in this algebraic proof, we need to apply the properties of equality and the knowledge that vertical angles are congruent.
Given:
Angle 1 = 3x + 20
Angle 2 = 5x - 16
Since Angle 1 and Angle 3 are vertical angles, they have the same measure.
a.) To find the measure of Angle 3, we substitute the measure of Angle 1 into the equation for Angle 3:
Angle 3 = Angle 1 = 3x + 20
So, _____ = 3x + 20 (Substitution)
b.) We are given that the measure of Angle 1 is equal to the measure of Angle 3. To find the missing term, we can equate the measures of Angle 1 and Angle 2:
3x + 20 = 5x - 16
To isolate the missing term on one side, we can use the subtraction property of equality:
-2x + 20 = -16
So, -2x + 20 = _____ (Subtraction Property of Equality)
c.) To further isolate the missing term on one side, we can use the subtraction property of equality again:
-2x + 20 - 20 = -16 - 20
-2x = -36
So, -2x = _____ (Subtraction Property of Equality)
d.) To solve for x, we need to divide both sides of the equation by -2:
(-2x) / -2 = (-36) / -2
x = 18
So, x = _____ (Division Property of Equality)
By following these steps and applying the properties of equality, we have determined the missing values in the algebraic proof.