Show that the sum of the measures of the interior angles of any quadrilateral is 360° by carrying out the following steps:

a. Draw any quadrilateral, as illustrated in Figure 7.41 (but draw your quadrilateral so it has a different shape from the one shown here).

Figure 7.41

b. What is the sum m∠1 + m∠2 + m∠3?

c. What is the sum m∠4 + m∠5 + m∠6?

d. The sum of the measures of the angles of the quadrilateral is (m∠1 + m∠2 + m∠3) + (m∠4 + m∠5 + m∠6). What is this sum?

e. Do you think this argument will apply for any quadrilateral?

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