Angle A = 60 degrees
Base angles of small isosceles triangles = 60 degrees each
Angle C = 120 degrees
Base angles of large isosceles triangle = 30 degrees each
Angle e = 120 degrees
Angle d = 60 degrees
Angle f = 120 degrees
Angle h = 60 degrees
To solve all the angles in the image, we can start by identifying all the triangles within the star.
We see four small isosceles triangles and one larger isosceles triangle.
Small isosceles triangle: In the small isosceles triangle on the left, we have the following:
Angle A, which is 60 degrees.
Two base angles, which are congruent and can be calculated using the following formula: (180 - angle A) / 2.
In this case, each base angle would be (180 - 60) / 2 = 60 degrees.
Large isosceles triangle: In the large isosceles triangle, we have the following:
Angle C, which is 120 degrees.
Two base angles, which are congruent and can be calculated using the same formula as the small triangle:
(180 - angle C) / 2 = (180 - 120) / 2 = 30 degrees.
Next, we can move on to the remaining angles:
Angle e: Angle e is located at the vertex of a small isosceles triangle and is supplementary to the base angle of 60 degrees.
Therefore, angle e = 180 - 60 = 120 degrees.
Angle d: Angle d is the exterior angle of a small isosceles triangle.
We can use the fact that the sum of the interior angles of a triangle is 180 degrees to solve for angle d.
In this case, angle d = 180 - (angle A + base angle) = 180 - (60 + 60) = 60 degrees.
Angle f: Angle f is formed by the intersection of two straight lines and is therefore a vertical angle.
Since vertical angles are congruent, angle f = angle e = 120 degrees.
Angle h: Angle h is formed by the intersection of two straight lines and is therefore a vertical angle.
Since vertical angles are congruent, angle h = angle d = 60 degrees.