Letters a, b, c, and d are angles measures. which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? check all that apply. a = c a = d c = d b + c = 180° b + d = 180°

When a line intersects two parallel lines, then corresponding angles are formed which means the same corners are congruent, So one of the options is c = d.

And because of vertical angles, a = d is also an answer. Lastly b+d=180, because b+c=180 an c=d therefore b+d=180. Thus the answer is B,C,E. which is a=d, c=d, and b+d=180. Hope this helps, and have a good day!

Hence,  lines and are parallel lines cut by transversal .

Step-by-step explanation:

Given: Letters are angles measures.

To prove: lines and are parallel lines cut by transversal .

From the figure:

                        (Vertically opposite angles)    

                        (Exterior opposite angles)    

                        (Corresponding angles)

             (Linear Pair angle property)

             (Co-exterior angles )

Here, Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of parallel lines.

are pair of corresponding angles then we can conclude that lines and are parallel lines cut by transversal .

Hence Proved.

Learn more about Parallel line and transversal line here:

link

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°