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?

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°