What is the m<R?​

128

Step-by-step explanation:

Hey There!

So the rule about interior angles of a trapezoid

is that the angles that lie on the segments that are not parallel are supplements

so essentially what I'm saying is that angle R and angle U are supplementary angles so to find x we do

180=15x+8+7x-4

step 1 combine like terms

15+7=22

8-4=4

now we have

180=22x+4

step 2 subtract 4 from each side

180-4=176

now we have

176=22x

step 3 divide each side by 22

176/22=8

so x=8

now we plug in 8 to 15x+8

8x15=120

120+8=128

so we can conclude that angle R = 128

∠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.