The measure of ∠ VWY is 40°
An equilateral triangle is a triangle in which all three sides have the same length.
Given that, Δ VWX and Δ XYZ are congruent equilateral triangles, and ∠ VXY is 80°.
We know that, each angle in an equilateral triangle is 60°
Therefore, m ∠ WXY = 60°+80° = 140°
Considering the Δ WXY,
WX ≅ XY (∵ Δ VWX ≅ Δ XYZ)
Therefore, ∠ YWX ≅ ∠ XYW (angle opposite to equal sides are equal)
Therefore, Δ WXY is an isosceles triangle,
Now, ∠ YWX + ∠ XYW + ∠ WXY = 180° (angle sum property of a triangle)
∠ YWX + ∠ YWX + ∠ WXY = 180°
2∠ YWX = 180° - 140°
∠ YWX = 40°/2
∠ YWX = 20°
Now, ∠ VWY = ∠ VWX - ∠ YWX
∠ VWY = 60°-20°
∠ VWY = 40°
Hence, The measure of ∠ VWY is 40°
For more references on equilateral triangles, click;
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Answer:
∠VWY = 60
Step-by-step explanation:
I asked a friend because he is a math genius. He didn't explain how though.
