Question

Part A Find the value of a in the parallelogram.

a=4
a = 17
a=7/3
a=9

Part B What is m Z
48°
64°
116°
132°

Answer 1

• a = 17
• ∠Z = 116°

Explanation:

You want the value of 'a' in a parallelogram with opposite sides marked (a+3) and (2-14). And you want the value of an unmarked angle in the same parallelogram with opposite angles marked (4b-56)° and (2b+4)°.

A. Sides

Opposite sides of a parallelogram are congruent, so we have ...

XY = WZ

(a +3) = (2a -14)

17 = a . . . . . . . . . . add 14-a

B. Angles

Opposite angles of a parallelogram are congruent, so we have ...

∠Y = ∠W

(4b -56)° = (2b +4)°

2b = 60 . . . . . . . . . . . . add 56-2b

Then angle W is ...

∠W = (2b +4)° = (60 +4)° = 64°

Angle Z is the supplement of angle W, so its measure is ...

∠Z = 180° -64°

∠Z = 116°

__

Additional comment

Adjacent angles in a parallelogram are supplementary.