Answer:
- Triangle 1 – ∠1 = 25°, ∠2 = 115° Triangle 2 – ∠1 = 25°, ∠3 = 40°
- Triangle 1 – ∠1 = 5°, ∠2 = 15° Triangle 2 – ∠2 = 15°, ∠3 = 160°
Step-by-step explanation:
You can save yourself some trouble if you realize that one of the angles in one pair must match one of the angles in the other pair.
This observation eliminates the first two choices.
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Going further, the triangles will be similar if the dissimilar angles together with one of the similar angles totals 180°.
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Triangle 1 – ∠1 = 50°, ∠2 = 30°
Triangle 2 – ∠2 = 20°, ∠3 = 100° . . . . . no angles match
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Triangle 1 – ∠1 = 60°, ∠2 = 20°
Triangle 2 – ∠1 = 40°, ∠3 = 100° . . . . . no angles match
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Triangle 1 – ∠1 = 25°, ∠2 = 115°
Triangle 2 – ∠1 = 25°, ∠3 = 40° . . . . 25° angles match; 25+40+115 = 180
These triangles are similar.
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Triangle 1 – ∠1 = 5°, ∠2 = 15°
Triangle 2 – ∠2 = 15°, ∠3 = 160° . . . . 15° angles match; 15+5+160 = 180
These triangles are similar.
