Question

solve for x. lines that appear parallel are parallel. show your work! 17. x = 18. x = 19. lines p and q are parallel. find the indicated angles. a. m∠1 = b. m∠2 = c. m∠5 = d. m∠4 = e. m∠9 = 20. if △cow≅△pig, and co = 25, cw = 18, ig = 23 and pg = 7x - 17. find the value of x. 21. if △def≅△heg, what is the value of x?

Explanation:

17.

Step1: Set up equation

Since the two angles are vertical - angles and vertical - angles are equal, we have $5x + 6=3x + 46$.

Step2: Isolate x terms

Subtract $3x$ from both sides: $5x-3x + 6=3x-3x + 46$, which simplifies to $2x+6 = 46$.

Step3: Isolate the variable

Subtract 6 from both sides: $2x+6 - 6=46 - 6$, getting $2x=40$.

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{40}{2}$, so $x = 20$.

Step1: Set up equation

Since the two angles are corresponding angles (for parallel lines) and corresponding angles are equal, we have $4x + 50=3x + 25$.

Step2: Isolate x terms

Subtract $3x$ from both sides: $4x-3x + 50=3x-3x + 25$, which gives $x+50 = 25$.

Step3: Solve for x

Subtract 50 from both sides: $x+50 - 50=25 - 50$, so $x=-25$.

Step1: Use congruence property

Since $\triangle COW\cong\triangle PIG$, corresponding sides are equal. So $PG = CW$.

Step2: Set up equation

We know that $CW = 18$ and $PG=7x - 17$, so $7x-17 = 18$.

Step3: Isolate x terms

Add 17 to both sides: $7x-17 + 17=18 + 17$, getting $7x=35$.

Step4: Solve for x

Divide both sides by 7: $\frac{7x}{7}=\frac{35}{7}$, so $x = 5$.

Answer:

$20$

18.