Name The Shape That Will Result From Connecting The Points (-4, 1) , (-4, -4) , (0, 3) , And (0, 6) .A:

The angles and their relationships are –

a) ∠x = 135° (corresponding angles), ∠y = 135° (vertical angles)

b) ∠y = 45° (liner pair angles), ∠x (not enough information provided)

c) ∠x = 135° (corresponding angles), ∠y = 45° (liner pair angles)

d) ∠x = 45° (liner pair angles), ∠y (not enough information provided)

What is angle pair relationship?

In Geometry, there are five fundamental angle pair relationships:

Complementary Angles

Supplementary Angles

Adjacent Angles

Linear Pair

Vertical Angles

a) In the first diagram –

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Similarly, ∠y = ∠x as they both are vertically opposite angles to each other.

So, ∠y = 135°.

b) In the second diagram –

∠y + ∠a =180° as they are both form a linear pair of angles.

So, ∠y = 180° – ∠a

∠y = 180° – 135°

∠y = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

c) In the third diagram –

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Now, ∠y + ∠x =180° as they are both form a linear pair of angles.

So, ∠y = 180° – ∠x

∠y = 180° – 135°

∠y = 45°.

d) In the fourth diagram –

∠x + ∠a =180° as they are both form a linear pair of angles.

So, ∠x = 180° – ∠a

∠x = 180° – 135°

∠x = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

Therefore, all the angles are and their relationships are found.

To learn more about angle pair relationship from the given link

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