## Triangle 1 has an angle that measures 62° and an angle that measures 14°. Triangle 2 has an angle that measures 14° and an angle that measur

Question

Triangle 1 has an angle that measures 62° and an angle that measures 14°. Triangle 2 has an angle that measures 14° and an angle that measures x°, where x ≠ 62º. Based on the information, Bob claims that triangle 1 and triangle 2 cannot be similar.
2. What value of x, in degrees, will refute Bob’s claim?

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1 week 2021-09-11T02:09:34+00:00 1 Answer 0

If x ≠ 62° and we want to Refute Bob’s claim that  Δ1 and  Δ2 cannot be similar, the value of x should be:

x = 104°

Step-by-step explanation:

Let’s recall that the interior angles of a triangle add up to 180°, therefore:

Δ 1 = ∠62° + ∠14° + ∠180° – (62° + 14°)

Δ 1 = ∠62° + ∠14° + ∠104°

Then,

Δ 2 = ∠x° + ∠14° + ∠180° – (x° + 14°)

Δ 2 = ∠x° + ∠14° + ∠166° – x°

If x ≠ 62° and we want to Refute Bob’s claim that  Δ1 and  Δ2 cannot be similar, the value of x should be:

x = 104°

Replacing with x = 104, in  Δ 2 = ∠x° + ∠14° + ∠166° – x°:

Δ 2 = ∠104° + ∠14° + ∠166° – 104°

Δ 2 = ∠104° + ∠14° + ∠62°