Respuesta :

C. X=5 y=22
This figure is a kite, which means the bottom two sides are congruent and the top two sides are congruent. With that in mind we can set (4x-3) = (2x+7). By doing a simply two-step rearrangement we find that X=5.
The other property associated with a kite figure is that the two side angles where the "top 2 sides" meet the "bottom two sides" are equal. So we find what angle measurement the two angles are supposed to make by adding the existing angles and subtracting from 360: [360-(79+61)=220]. So we know that the "5y" angle is supposed to take up half of this 220 since there are two of these angles which are congruent (I know it sounds confusing but it you draw this out as you read it then it'll make more sense. PICTURES ALWAYS HELP). So in order to find y, we set 5y=110, and we find that y=22

Answer:

The value of x and y is 5 and 22 respectively

Option C is correct.

Step-by-step explanation:

Given the figure

BC=2x+7, AB=4x-3, AD=CD, ∠ABC=79° and ∠BCD=(5y)°

we have to find the values of x and y.

As in given figure AD=CD

which implies the figure ABCD is kite.

Two disjoint pairs of consecutive sides of kite are congruent, AB=BC

∴ [tex]2x+7=4x-3[/tex]

[tex]4x-2x=7+3=10[/tex]

[tex]2x=10[/tex]

[tex]x=5[/tex]

As the non-vertex angles of a kite are congruent.

⇒ ∠BAD=∠BCD=(5y)°

Now as ABCD is a quadrilateral therefore by angle sum property of quadrilateral, the sum of all angles of quadrilateral equals to 360°

∠A+∠B+∠C+∠D=360°

5y+79°+5y+61°=360°

10y=220°

y=22

Hence, the value of x and y is 5 and 22 respectively.

Option C is correct.

                     

Otras preguntas