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UNDERSTANDING QUADRILATERALS 1 41

B

D

w

8

P

3. As before consider quadrilateral ABCD (Fig 3.6). Let P be any

point in its interior. Join Pto vertices A, B, C and D. In the figure,

consider APAB. From this we see x = 180º – m22 - mZ3;

similarly from APBC, y = 180º-m24-m25, from APCD,

2 = 180° - m26 - m27 and from APDA, w = 180° - mZ8

- mZ1. Use this to find the total measure mZ1 + m2 + ...

+ m28, does it help you to arrive at the result? Remember

2x + 2y + 2x + Zw = 360°

These quadrilaterals were convex. What would happen if the

А

Fig 3.6

B

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