In the diagram below, bd is parallel to xy. what is the value of y? (apex)

85°

Step-by-step explanation:

y and the given angle are alternate interior angles. Alternate interior angles are congruent where parallel lines are crossed by a transversal.

Value of y = 85°.

Step-by-step explanation:

In the diagram, two parallel lines BD and XY and a transversal line.

When the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.

And alternate interior angles are always same in measure.

So,

Angle y and angle 85 are alternate interior angles and both are same.

y = 85°

That's the final answer.

I hope it will helps you.

∠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.

correct answer is option b.

step-by-step explanation:

the true statement about geometric figure is option b that is one line can be drawn through all three points.

if three points are on the same plane, they can be connected by a line.