geometry

Consider the interior Quadrilateral as WXYZ
the corresponding interior angles will be angW=180- ext(angleW)
angX=180- ext(angleX)
angY=180- ext(angleY)
angZ=180- ext(angleZ)

As it is a Quadrilateral sum of the angles equals to 360

angW+angX+angY+angZ=360

thus we get
ext(angleW)+ext(angleX)+ext(angleY)+ext(angleZ)=360

thus from Stmt 1 and Stmt 2 we have ext(angleZ)+ext(angleW)
thuis we can find ext(angleX)+ext(angleY)

gauravgundal wrote:Consider the interior Quadrilateral as WXYZ
the corresponding interior angles will be angW=180- ext(angleW)
angX=180- ext(angleX)
angY=180- ext(angleY)
angZ=180- ext(angleZ)

As it is a Quadrilateral sum of the angles equals to 360

angW+angX+angY+angZ=360

thus we get
ext(angleW)+ext(angleX)+ext(angleY)+ext(angleZ)=360

thus from Stmt 1 and Stmt 2 we have ext(angleZ)+ext(angleW)
thuis we can find ext(angleX)+ext(angleY)

I don't get it.. Can you give a more detailed explanation???

Consider angle w an angle supplementary to one of the angle measures of the quadrilateral.

Also, consider angle z an angle supplementary to one of the angle measures of the quadrilateral.

1. w = 95, so its supplementary angle must be 105. We know that 105 is one of the measures of an interior angle in the quadrilateral. We still cannot calculate x + y. INSUFFICIENT.

2. z = 125, so so its supplementary angle must be 55. We know that 55 is one of the measures of an interior angle in the quadrilateral. We still cannot calculate x + y. INSUFFICIENT.

Together, we know that 105 and 55 are two of the interior angle measures of the quadrilateral. We know that, by definition, all quadrilaterals' interior angles total 360 degrees.

105 + 55 = 160. So we know that the other two interior angles of the quadrilateral total 360 - 160 = 200 degrees. Even though this total does not directly correspond to the sum of x and y, which are not interior angles of the quadrilateral, they are supplementary angles.

Imagine if the interior angle supplementary to x was 115. x would be 65.

Then imagine that the angle supplementary to y was 85. y would be 95.

It doesn't matter if we know what the missing interior angles are by themselves. We know they total 200 degrees, so x and y total 160 degrees.

Answer is C.

jjk wrote:Consider angle w an angle supplementary to one of the angle measures of the quadrilateral.

Also, consider angle z an angle supplementary to one of the angle measures of the quadrilateral.

1. w = 95, so its supplementary angle must be 105. We know that 105 is one of the measures of an interior angle in the quadrilateral. We still cannot calculate x + y. INSUFFICIENT.

2. z = 125, so so its supplementary angle must be 55. We know that 55 is one of the measures of an interior angle in the quadrilateral. We still cannot calculate x + y. INSUFFICIENT.

Together, we know that 105 and 55 are two of the interior angle measures of the quadrilateral. We know that, by definition, all quadrilaterals' interior angles total 360 degrees.

105 + 55 = 160. So we know that the other two interior angles of the quadrilateral total 360 - 160 = 200 degrees. Even though this total does not directly correspond to the sum of x and y, which are not interior angles of the quadrilateral, they are supplementary angles.

Imagine if the interior angle supplementary to x was 115. x would be 65.

Then imagine that the angle supplementary to y was 85. y would be 95.

It doesn't matter if we know what the missing interior angles are by themselves. We know they total 200 degrees, so x and y total 160 degrees.

Answer is C.

gotcha.. thanks!