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Citrus2011 [14]
3 years ago
7

Letters a, b, c, and d are angles measures. Lines m and n are cut by transversal p. At the intersection of lines p and m, labele

d clockwise, from uppercase left, the angles are: a, b, c, blank. At the intersection of lines p and n, labeled clockwise, from uppercase left, the angles are: blank, blank, d, blank. Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options. a = c a = d c = d b + c = 180° b + d = 180°
Mathematics
2 answers:
laiz [17]3 years ago
7 0

Answer:

B, C, and E

Step-by-step explanation

hi

Nataliya [291]3 years ago
5 0

Answer:

i. a = c

ii. c = d

iii. b + d = 180°

Step-by-step explanation:

A transversal is a line that intersects a line or two parallel lines, forming a series of  congruent angles.

In the description given, the following could be referred:

a = c (vertically opposite angle property)

c = d (vertically opposite angle property)

c + b = 180^{0} (sum of angles on a straight line)

b + d = 180^{0} (sum of angles on a straight line)

But the required equation for the prove are: a = c, c = d and b + d = 180^{0}.

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The sum of the ages of Kristen and Ben is 32. Four years ago Kristen was twice as old as Ben. How old are they both now?
Elan Coil [88]

Let us say that:

K = age of Kristen

B = age of Ben

 

From the problem, we make the equations:

eqtn 1: K + B = 32

eqtn 2: (K – 4) = 2 (B – 4)

 

Simplifying eqtn 2:

K – 4 = 2 B – 8

K = 2 B – 4

 

Plugging in this to eqtn 2:

(2 B – 4) + B = 32

3 B – 4 = 32

3 B = 36

B = 12

 

From eqtn 2:

K = 2 B – 4 = 2 (12) – 4 = 20

 

So Kristen is 20 while Ben is 12.

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