I tried solving it and I didn’t get the right answer can someone explain to me

X=29°

Step-by-step explanation:

Since triangles ABC and DEC are congruent, Angle A = Angle D = 74°

Sum of all angles in a triangle is 180°

So, Angle A + Angle B + Angle C =180°

74°+2X+48°=180°

2X=180°-122°

2X=58°

X=29°

Explanation:

When it comes to congruence statements like this, the order of the letters is important. This is so we pair up the letters properly.

ABC has A first, B second, C third

DEC has D first, E second, C third

So we have these pairings

Which leads to

Due to the fact that congruent triangles have congruent corresponding parts.

Since B = E and B = 2x, we can say that E = 2x by either substitution or the transitive property. Both effectively say the same thing.

Now focus on triangle CDE

The three angles we have are

Those three angles add to 180. This is true for any triangle.

C+D+E = 180

48+74+2x = 180

122+2x = 180

2x = 180-122

2x = 58

2x = 58/2

x = 29

Side note: since x = 29, this means angle B = 2x = 2*29 = 58, and this is the measure of angle E as well.

We can check the answer by doing C+D+E = 48+74+58 = 180. So we have confirmed the answer.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

dd

step-by-step explanation:

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