Help with Holiday Homework (1 Viewer)

[FroZenWaffleS]

Have a number of questions from my textbook (Maths in Focus Extension) that I cant figure out.

A(2,-1) , B(-3,4) and C(1,-5) form the vertices of a triangle. Find the interior angles of the triangle. (Used the angle between two lines formula but didnt work)

A(0,0) , B(1,2) , C(5,2) and D(4,0) form the vertices of a parallelogram.
By finding all the interior angles, show that opposite angles are equal.
Find the obtuse angle between the diagonals of the parallelogram.

Post more later

 

[Will Hunting]

A(2,-1) , B(-3,4) and C(1,-5) form the vertices of a triangle. Find the interior angles of the triangle. (Used the angle between two lines formula but didnt work)

One of the angles could be obtuse, in which case tanΘ will be negative (i.e. lose the absolute value signs from the RHS)

Sketeching this Δ, it can be seen that the obtuse interior angle occurs at the vertex, (2,-1). Drop the absolute value signs off your ∠ between two lines formula for this point and solve for Θ.

A(0,0) , B(1,2) , C(5,2) and D(4,0) form the vertices of a parallelogram.
By finding all the interior angles, show that opposite angles are equal.
Find the obtuse angle between the diagonals of the parallelogram.

Going out to dinner I'll get back to you on this

 

[jumb]

A(2,-1) , B(-3,4) and C(1,-5) form the vertices of a triangle. Find the interior angles of the triangle. (Used the angle between two lines formula but didnt work)

A(0,0) , B(1,2) , C(5,2) and D(4,0) form the vertices of a parallelogram.
By finding all the interior angles, show that opposite angles are equal.
Find the obtuse angle between the diagonals of the parallelogram.

For both of these questions, find the gradients with the two point formula (m = (y2-y1)/(x2-x1)) and the angle formula: tan(theta) = (m1-m2)/(1+m1m2)

Your answer from the angle one will be either acute or obtuse. Obviosuly, find the supplement angle if the answer is the wrong one.