Question

WXYZ is a parallelogram find the angle measures

Answer 1

Answer:

W and Y = 91. X and Z = 89

Step-by-step explanation:

Those two angles will add to 180.

5a - 21 + 3a + 25 = 8a + 4

8a + 4 = 180

8a = 176

176 / 8 = 22 = a

Plug in a for an angle.

3(22) + 25 = 91

180 - 91 = 89

Answer 2

The properties of a parallelogram indicate the value of sum of ∠X and

∠W.

Response:

• ∠W = 91°

• ∠X = 89°

• ∠Y = 91°

• ∠Z = 89°

What are the properties of a parallelogram that can be used to find the angles?

Given that WXYZ is a parallelogram, we have;

Adjacent angles are supplementary, which gives;

(5·a - 21)° + (3·a + 25)° = 180°

(8·a + 4)° = 180°

8·a = 180° - 4° = 176°

$a = \dfrac{176}{8} = \mathbf{ 22}$

a = 22

∠X = (5 × 22 - 21)° = 89°

∠W = (3 × 22 + 25)° = 91°

Opposite angles of a parallelogram are equal.

Therefore;

∠X = ∠Z = 89°

∠W = ∠Y = 91°

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