Abcd is a rhombus. find each measure. find ab and find m/abc

x= 13/3

y=7.5

AB is 97/3

ABC is 122

Step-by-step explanation:

A rhombus is a special type of quadrilateral that has 4 equal sides and perpendicular diagonals which bisect each other and the angles. Knowing this then 4x+15 is equal to 7x+2 and 12y is equal to 90. Solve for each variables then substitute as needed to find the remaining values.

4x+15=7x+2

15=3x+2

13=3x

13/3 = x

BC is 4x+15 = 4(13/3)+15 = 52/3 + 45/3 = 97/3

CD is 7x+2 = 7(13/3)+2 = 91/3 + 6/3 = 97/3

Now solve for 12y=90 and y = 7.5.

Angle AFB is 12(7.5) = 90

Angle BCF is 4y-1 = 4(7.5)-1 = 29

Since the diagonal bisects the angle this means angle BCD is 58. So angle ABC will be 180-58 = 122

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

asdsad

step-by-step explanation: