Grade 6 Angles Test worksheet - Free Printable

Let's solve each part of the problem step by step.

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Part 1: Find x in the first diagram

We have a straight line with an angle of 34° and another angle labeled x, forming a linear pair (they are adjacent angles on a straight line).

> Linear Pair Theorem: The sum of angles on a straight line is 180°.

So:
$$
x + 34^\circ = 180^\circ
$$
$$
x = 180^\circ - 34^\circ = 146^\circ
$$

✔ Answer: $ x = 146^\circ $

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Part e: Triangle ABC, find ∠ACB

We are given:

- $ \angle B = 30^\circ $
- Exterior angle at C is $ 120^\circ $
- We need to find $ \angle ACB $, which is the interior angle at C.

#### Step 1: Use exterior angle property

> Exterior Angle Theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

But here, we can use the fact that:
$$
\text{Interior angle at } C + \text{Exterior angle at } C = 180^\circ
$$
$$
\angle ACB + 120^\circ = 180^\circ
$$
$$
\angle ACB = 180^\circ - 120^\circ = 60^\circ
$$

✔ So, $ \angle ACB = 60^\circ $

Now, let’s verify using triangle angle sum:

We already know:
- $ \angle B = 30^\circ $
- $ \angle C = 60^\circ $
- Sum of angles in a triangle = $ 180^\circ $

So:
$$
\angle A = 180^\circ - 30^\circ - 60^\circ = 90^\circ
$$

So $ x = \angle A = 90^\circ $

But the question only asks for $ \angle ACB $, so:

✔ Answer: $ \angle ACB = 60^\circ $

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Part f: Regular quadrilateral — find exterior angles w, x, z, y

A regular quadrilateral means all sides and angles are equal. That is a square.

In a square:
- Each interior angle = $ 90^\circ $
- Each exterior angle = $ 180^\circ - 90^\circ = 90^\circ $

Because:
- Exterior angle = $ 180^\circ - \text{interior angle} $
- And since it's regular, all exterior angles are equal.

So:
- $ w = 90^\circ $
- $ x = 90^\circ $
- $ y = 90^\circ $
- $ z = 90^\circ $

> Note: The labels w, x, z, y likely refer to the four exterior angles at the vertices (in order), but since it's regular, they're all the same.

✔ Answers:
- $ w = 90^\circ $
- $ x = 90^\circ $
- $ y = 90^\circ $
- $ z = 90^\circ $

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✔ Final Answers:

First diagram:
- $ x = 146^\circ $

e. $ \angle ACB = 60^\circ $

f. Regular quadrilateral:
- $ w = 90^\circ $
- $ x = 90^\circ $
- $ y = 90^\circ $
- $ z = 90^\circ $

Let me know if you'd like this formatted for a worksheet!