A quadrilateral is divided into three triangles as shown. We know that the sum of the angles of each triangle is 180°. The
sum of the angles at the vertices of the quadrilateral is
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Answer:
Firstly, since you haven't provided any information on the data that you already possess, I'm going to assume that:
You know the values of the other 3 angles. In this case, the test condition is easy to solve:
Consider a quadrilateral ABCD, whose 4 angles are ∠A,∠B,∠C and ∠D.If ∠A+∠B+∠C=180∘,then ∠D=180∘
You know the coordinates of the 4 vertices. In this case, the test condition is satisfied if:
Consider a quadrilateral ABCD, with the coordinates of its 4 points as A(xa,ya,za),B(xb,yb,zb),C(xc,yc,zc),and D(xd,yd,zd).Use the distance formula to calculate AB, BC, CA, AD, diagonals AC and BD.Now, if any two sides add up to a diagonal, you have the angle between those 2 sides as 180∘For your information, the distance formula isD(P1,P2)=(x2−x1)2+(y2−y1)2+(z2−z1)2−−−−−−−−−−−−−−−−−−−−−−−−−−−−√,where P1=(x1,y1,z1),and P2=(x2,y2,z2)
I hope this answers your question, and I suggest that if it didn't answer your question, please clearly state exactly what data you are facilitated with.
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Answer:
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