CPM Homework Help : CC1MN Problem 10-109

A quadrilateral where all 4 sides are extended toward the left. The first interior angle, 93 degrees has an exterior angle, a. The second interior angle, 97 degrees has an exterior angle, b. The third interior angle, 84 degrees, has an exterior angle, c. The final interior angle is unknown, but the exterior angle is, d. The exterior angles of a quadrilateral are labeled $a, b, c$ , and $d$ in the diagram at right. Find the measures of $a, b, c,$ and $d$ and then find the sum of the exterior angles.

Hint:

The missing exterior angles each form a straight angle with an interior angle.
What is the measure of a straight angle?

More help:

You will need to find the angle that forms a linear pair with $\angle d$ .
If a quadrilateral can be made into two triangles, what is the sum of the interior angles of a quadrilateral?

Answer:

$a = 87º, b = 83°, c = 96° d = 94º$ ,
$\angle a + \angle b + \angle c + \angle d = 360º$