Question

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

Answer 1

Answer:

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°

Answer 2

Answer:  x = 29

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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

• A pairs with D
• B pairs with E
• C pairs with C (ie it pairs with itself)

Which leads to

• A = D
• B = E
• C = C

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.

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Now focus on triangle CDE

The three angles we have are

• C = 48
• D = 74
• E = 2x

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

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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.