Parallelogram abcd is a rectangle. ac=6y−1 bd=4y+13 what is the value of y? enter your answer in the box. y= a rectangle a b c d. side a b and side c d are parallel. side a d and b c are parallel. diagonal b d and a c intersect each other at a point labeled as x.

The value of y is: 7

Step-by-step explanation:

The figure of the rectangle ABCD is attached to the answer.

We are given that Parallelogram ABCD is a rectangle.

AC=6y−1

BD=4y+13

Diagonal BD and AC intersect each other at a point labeled as X.

Also we know that: The two diagonals of a rectangle are equal in length and bisect each other.

i.e. length of AC=BD

Hence 6y-1=4y+13

⇒   6y-4y=13+1

 ⇒  2y=14

  ⇒  y=7

Hence, AC=6×7-1=42-1=41

      BD=4×7+13=41

Hence, the value of y is 7.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.