Question

Jenna drew irregular quadrilateral ABCD inscribed in circle P. She knows that: m∠3=2⋅m∠1, and m∠2=2⋅m∠4, and m∠2+m∠3=360°. What generalization can she make from her work?

Answer 1

Answer:

The generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

Step-by-step explanation:

We are given the following from what she knows

m∠3=2⋅m∠1... 1

m∠2=2⋅m∠4 ... 2

m∠2+m∠3=360 ... 3

From what is given, we can substitute equation 1 and 2 into equation 3 as shown:

From 3:

m∠2+m∠3=360

Substituting 1 and 2 we will have:

2⋅m∠4 + 2⋅m∠1 = 360

Factor out 2 from the left hand side of the equation

2(m∠4+m∠1) = 360

Divide both sides by 2

2(m∠4+m∠1)/2 = 360/2

m∠4+m∠1 = 180°

Since the sum of two supplementary angles is 180°, hence the generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°