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: Use corresponding - angles property

Since the lines are parallel, the corresponding angles are equal. So, \(5x + 6=3x + 46\).

Step2: Isolate the variable \(x\)

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

Step3: Solve for \(x\)

Subtract 6 from both sides: \(2x+6 - 6=46 - 6\), so \(2x=40\). Then divide both sides by 2: \(x = 20\).

Step1: Use corresponding - angles property

Since the lines are parallel, the corresponding angles are equal. So, \(4x + 50=3x + 25\).

Step2: Isolate the variable \(x\)

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 the property of congruent triangles

If \(\triangle COW\cong\triangle PIG\), then the corresponding sides are equal. So, \(PG = CW\).

Step2: Set up the equation

We know that \(CW = 18\) and \(PG=7x - 17\), so \(7x-17 = 18\).

Step3: Solve for \(x\)

Add 17 to both sides: \(7x-17 + 17=18 + 17\), which gives \(7x=35\). Then divide both sides by 7: \(x = 5\).

Answer:

\(x = 20\)

18.