Angie and becky each completed a separate proof to show that the measures of vertical angles akg and hkb are equal. who completed the proof incorrectly? explain.

line ab intersecting line gh at k

angie's proof

statement justification
1. segment gh intersects segment ab at k 1. given
2. m∠akg + m∠gkb = 180°
m∠gkb + m∠hkb = 180° 2. definition of supplementary angles
3. m∠akg + m∠ gkb = m∠gkb + m∠hkb 3. substitution property
4. m∠akg = m∠hkb 4. subtraction property

becky's proof

statement justification
1. segment gh intersects segment ab at k 1. given
2. m∠akg + m∠gkb = 180°
m∠gkb + m∠hkb = 180° 2. angle addition postulate
3. m∠akg + m∠ gkb = m∠gkb + m∠hkb 3. substitution property
4. m∠akg = m∠hkb 4. subtraction property

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.