Question

given: $angle1congangle3$, $mangle1 = 5x - 7$, $mangle3 = 2x + 5$ prove: $x = 4$ statements reasons a.) $angle1congangle3$, $mangle1 = 5x - 7$, $mangle3 = 2x + 5$ a. _ b.) $mangle1 = mangle3$ b. _ c.) $5x - 7 = 2x + 5$ c. _ d.) $3x - 7 = 5$ d. _ e.) $3x = 12$ e. ___

Explanation:

Step1: Given information

Given that $\angle1\cong\angle3$, $m\angle1 = 5x - 7$, $m\angle3=2x + 5$.

Step2: Definition of congruent angles

If two angles are congruent, their measures are equal. So $m\angle1=m\angle3$.

Step3: Substitution property

Substitute $m\angle1 = 5x - 7$ and $m\angle3=2x + 5$ into $m\angle1=m\angle3$, we get $5x - 7=2x + 5$.

Step4: Subtract 2x from both sides

Subtracting $2x$ from both sides of $5x - 7=2x + 5$ gives $3x-7 = 5$ (Subtraction property of equality).

Step5: Add 7 to both sides

Adding 7 to both sides of $3x - 7=5$ gives $3x=12$ (Addition property of equality).

Step6: Divide both sides by 3

Dividing both sides of $3x = 12$ by 3 gives $x = 4$ (Division property of equality).

Answer:

a. Given
b. Definition of congruent angles
c. Substitution property
d. Subtraction property of equality
e. Addition property of equality