Question

Analyze the diagram below and complete the instructions that follow. Find the values of x and y. Using those values, explain what is wrong with the figure above.

Answer 1

I have not done that yet cause i'm only a sophomore.

Answer 2

Answer:

The value of x is 12 and the value of y is 23. The given figure wrong because the vertically opposite angles are not same.

Step-by-step explanation:

From the given graph it is clear that lines XY and WZ intersect each other at point A and make 4 angles.

The angle XAZ and angle ZAY are supplementary angles because they lie on a straight line.

$\angle XAZ+\angle ZAY=180$

$6x+35+8x-23=180$

$14x+12=180$

$14x=168$

$x=12$

The value of x is 12.

The angle XAW and angle WAY are supplementary angles because they lie on a straight line.

$\angle XAW+\angle WAY=180$

$3y+y+88=180$

$4y+88=180$

$4y=92$

$y=23$

The value of y is 23.

The value of x is 12 and the value of y is 23, so the measure of all angles are

$\angle XAZ=6x+35=6(12)+35=107$

$\angle ZAY=8x-23=8(12)-23=73$

$\angle XAW=3y=3(23)=69$

$\angle WAY=y+88=23+88=111$

If two line intersect each other then the vertically opposite angles are always same. But here vertically opposite angles are not same.

$\angle XAZ\neq \angle WAY$

$\angle ZAY\neq \angle XAW$

Therefore the given figure wrong because the vertically opposite angles are not same.