ABCDE is a regular pentagon. FAD is an equilateral triangle, such that points F and E are on the same side of line AD. What is the measure (in degrees) of ∠FAB?
To find the measure of ∠FAB, we need to consider the properties of a regular pentagon and an equilateral triangle.
Since ABCDE is a regular pentagon, all its interior angles are congruent. The sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. In the case of a regular pentagon, each interior angle measures (5-2) * 180 / 5 = 108 degrees.
FAD is an equilateral triangle. In an equilateral triangle, all angles are congruent and measure 60 degrees.
Since AF is a side of both the pentagon and the triangle, FAB is an interior angle of the pentagon. Therefore, we can subtract the measure of ∠FAD from the measure of an interior angle of the pentagon to find the measure of ∠FAB.
∠FAB = ∠FAD - ∠BAD
Since ∠FAD is 60 degrees and we know that ∠BAD is an interior angle of the pentagon, we can calculate ∠FAB as follows:
∠FAB = 108 degrees - 60 degrees
∠FAB = 48 degrees
Therefore, the measure of ∠FAB is 48 degrees.
To find the measure of angle ∠FAB, we need to understand the properties of regular pentagons and equilateral triangles.
A regular pentagon has five sides of equal length and five angles of equal measure. In a regular pentagon ABCDE, each interior angle measures (5-2) × 180° / 5 = 108°.
An equilateral triangle has all three sides of equal length and all three angles of equal measure, which is 60°.
Now, let's analyze the given information. ∠FAD is an equilateral triangle, so ∠FAD measures 60°.
Since ABCDE is a regular pentagon, each interior angle measures 108°. Therefore, ∠ABD = ∠DAB = (180° - ∠BAD) / 2 = (180° - 108°) / 2 = 72°.
To find ∠FAB, we can subtract the known angles from ∠ABD: ∠FAB = ∠ABD - ∠BAD = 72° - 60° = 12°.
Thus, the measure of ∠FAB is 12°.
angle AED = 108, so EAD = 36
FAD = 60, so FAE = 24
so, FAB = FAE+EAB = 24+108 = 132