Question

I need to find y and z

for y-
24

45

27

135

for z-
135
98
82
90

Answer 1

• y = 27°
• z = 98°

Explanation:

The interior angle marked 5y is the supplement of the adjacent exterior angle marked 45°.

5y + 45° = 180°

5y = 135° . . . . . . . . subtract 45

y = 27° . . . . . . . . divide by 5

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The sum of the interior angles of a pentagon is (5-2)(180°) = 540°.

90° +5y +z +82° +135° = 540°

Using y=27°, we can subtract 442° from both sides to get ...

z = 98°

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Additional comment

You might recognize that the downward-sloping diagonal sides of the figure are parallel, so z and 82° are consecutive interior angles, hence supplementary. This fact means you don't have to be concerned with the other three angles in the figure to find the value of z: 180° -82° = 98°.