Triangles and their properties of Angles worksheet - Free Printable

Let's solve each part of Question 1 step by step, using the properties of triangles and angles.

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(a) – Already Solved as Example:

Given:
- Two angles: 35° and 45°
- Find ∠x

Solution:
Sum of angles in a triangle = 180°
So:
$$
∠x = 180° - 35° - 45° = 101°
$$
✔ Correct.

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(b)

Given:
- Two angles: 52° and 38°
- Find ∠x (the third angle in the triangle)

Solution:
$$
∠x = 180° - 52° - 38° = 90°
$$

✔ So, ∠x = 90°

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(c)

This is about an exterior angle of a triangle.

Given:
- Interior angles: 82° and 74°
- The angle labeled x is the exterior angle at the third vertex.

Rule:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

So:
$$
∠x = 82° + 74° = 156°
$$

✔ So, ∠x = 156°

> Note: The example box shows this calculation, so it's correct.

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(d)

Given:
- Right triangle (one angle is 90°)
- One acute angle is 42°
- Angle x is an exterior angle at the base (adjacent to the 90° angle)

We need to find ∠x, which is an exterior angle at the bottom-left corner.

First, let’s find the missing interior angle:

In the triangle:
- One angle = 90° (right angle)
- One angle = 42°
- So, the third interior angle =
$$
180° - 90° - 42° = 48°
$$

Now, ∠x is the exterior angle adjacent to this 48° angle.
Since they form a straight line:
$$
∠x = 180° - 48° = 132°
$$

Alternatively, you can use the exterior angle rule:
Exterior angle = sum of two non-adjacent interior angles
So:
$$
∠x = 90° + 42° = 132°
$$

✔ So, ∠x = 132°

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✔ Final Answers:

(b) ∠x = 90°
(c) ∠x = 156°
(d) ∠x = 132°

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Summary of Concepts Used:

1. Triangle Angle Sum: The sum of internal angles in a triangle is always 180°.
2. Exterior Angle Theorem: An exterior angle equals the sum of the two non-adjacent interior angles.
3. Straight Line: Angles on a straight line add up to 180°.

Let me know if you'd like a diagram explanation!