Answer:
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°
The value of x should be 62° or 104° for the triangles to be similar triangles, while anything else for the triangles to be not similar triangles.
Similar triangles are those triangles whose corresponding sides are in ratio and corresponding angles are of equal measures.
We know about similar triangles and in the given triangles 14° is a similar angle since the angle x can have a value equal to 62° therefore, Bob's claim is wrong triangles 1 and 2 can be similar triangles.
We want the angles to be similar angles therefore, for any value of x except 62° and 104°, angles will not be similar to each other.
Hence, the value of x should be 62° or 104° for the triangles to be similar triangles, while anything else for the triangles to be not similar triangles.
Learn more about Similar triangles:
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