The **equilateral triangle**, and regular **pentagon**, gives the measure of the

angles formed from which the interior angles of ABCF can be found.

Response:

<h3>Which properties of figures can be used to find the interior angles?</h3>

The **given **parameters are;

The** point** in the regular **pentagon **is point <em>F</em>

**ΔABF** is an **equilateral triangle**

**Required**:

The angles in quadrilateral** ABCF**

**Solution**:

Given that ΔABF is an equilateral triangle, we have;

∠FBA = ∠BAF = ∠AFB =** 60°**

∠ABC = An **interior angle** of a **regular **pentagon = 108°

Which gives;

∠BCF = ∠BFC = **Base **angles of an **isosceles **triangle **ΔBCF**

Which gives;

∠BCF + ∠BFC + 60° + 60° + 108° = 360°, **angle sum property** of a quadrilateral

2·∠BCF + 60° + 60° + 108° = 360°

2·∠BCF = 360° - (60° + 60° + 108° ) = **132°**

∠BCF = 132° ÷ 2 = **66°**

The interior angles of quadrilateral ABCF are;

- ∠CFA = 66° + 60° = <u>126°</u>

Learn more about **pentagons **here:

brainly.com/question/535962