Can someone tell me whats the missing information?
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)
Given: AD=AB
AE= AD/3
AF= AB/3
Prove: AE= AF
To find the missing information, we can use the fact that angles 1 and 3 are vertical angles, which means they are congruent. From the given information, we know that angle 1 is equal to 3 times x + 20, and since angle 1 is congruent to angle 3, we can set up an equation:
3x + 20 = angle 3 (Equation for angle 1)
a.) To find the missing information, we substitute the expression for angle 3 into the equation:
3x + 20 = (5x - 16)
b.) To solve for the missing information, we can use the subtraction property of equality. We want to isolate the missing information on one side of the equation, so we can start by subtracting 3x from both sides:
-3x + 3x + 20 = (5x - 16) - 3x
20 = 5x - 16
c.) Next, we can simplify the equation by adding 16 to both sides:
20 + 16 = 5x - 16 + 16
36 = 5x
d.) Finally, we can use the division property of equality to solve for x by dividing both sides of the equation by 5:
36 / 5 = 5x / 5
x = 36/5
Therefore, the missing information is:
a.) 5x - 16
b.) -2x + 20
c.) -2x
d.) x = 36/5