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Please help me geometry sucks!
Question is in the picture.

Please help me geometry sucks! Question is in the picture.-example-1
User RatDon
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1 Answer

2 votes

Answer:

A. 69°

Explanation:

Pre-Solving

We are given that pentagon ABCDE is congruent to pentagon FGHIJ.

We want to find the measure of ∠3.

Looking at the picture, we can see that ∠3 is at the vertex labeled 'B', so another name for ∠3 is ∠B.

Recall that when naming congruent shapes, the order of the letters matters, because each letter must correspond to another letter in the other shape. In other words, the vertex A corresponds to the vertex F in the two pentagons and so on.

  • The corresponding vertices means that ∠A ≅ ∠F and etc.

Solving

To start, let's look at the corresponding vertex to B.

The letter should be in the same place as where B is in ABCDE. In FGHIJ, that letter is G.

This means that vertex that corresponds to B is vertex G, which therefore means that ∠B ≅ ∠G.

We can also look to see that m∠G = 69°.

Because ∠B is congruent to this angle, the measure of ∠B is also 69°. Furthermore, since ∠B is another name for ∠3, this means that the measure of ∠3 is 69°.

So, the answer is A.

User Alexander Vassilev
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