Abcde is a regular pentagon .find the angles of a triangle ADC?
all the angles of the pentagon are 108°
∆ABC and ADE are isosceles, with angles of 108,36,36°
So, ∆ADC is isosceles with angles of 72,72,36°
To find the angles of a triangle ADC formed by an regular pentagon ABCDE, we need to use the properties of a regular pentagon.
A regular pentagon has five equal sides and five equal angles. Since ABCDE is a regular pentagon, all of the angles in the pentagon are equal to each other.
To find the measure of angle ADC, we first need to determine the measure of each angle in the pentagon.
Since a regular pentagon has five angles that sum up to 540 degrees (since the sum of all angles in a polygon can be found using the formula: (n-2)*180, where n is the number of sides), we divide 540 degrees by 5 to find the measure of each angle.
540 degrees ÷ 5 = 108 degrees
Therefore, each angle in the regular pentagon ABCDE measures 108 degrees.
Now, to find the measure of angle ADC, we need to consider that in triangle ADC, two of the angles are known: angle A and angle C. Both of these angles are equal to the angles in the regular pentagon.
So, angle ADC = angle A + angle C = 108 degrees + 108 degrees = 216 degrees.
Therefore, the measure of angle ADC in triangle ADC is 216 degrees.