A medicinal plant garden owner decided to construct a track along the side of the triangular area and three exit tracks. His friend suggested him that the ratio of an exterior angle at which the exit track formed must be in 21:25:26 for the beauty of region and easiness of pedestrian. Find the values of interior and exterior angles at which exit track would be constructed.
Answers
Answer:
Exterior 105° , 125° , 130°
Interior 75° , 55° , 50°
Step-by-step explanation:
Sum of exterior angles of a triangle = 360°
21 : 25 : 26 is ratio of exterior angles
let say angles are
21x , 25x & 26x
Sum = 21x + 25x + 26x = 72x
72x = 360°
=> x = 5
Exterior Angles = 21 * 5 = 105°
25 * 5 = 125°
26 * 5 = 130°
Interior angles = 180° - 105° = 75°
180° - 125° = 55°
180° - 130° = 50°
Exterior 105° , 125° , 130°
Interior 75° , 55° , 50°
Answer: Exterior angles are 105°, 125°, 130°
Interior angles are 75°, 55° , 50°
Step-by-step explanation:
Let the common ratio = x
the exit gates are in the ratio of Exterior angles
As we know the sum of exterior angle is 360°
Therefore
Exterior angles Corresponding interior angles
First angle = 21 x 5 = 105° 180 - 105 = 75°
second angle = 25 x 5 = 125 ° 180- 125= 55°
third angle = 26 x 5= 130° 180 - 130= 50°
Hence, exterior angles are 105°, 125°, 130° and interior angles are 75°, 55° , 50° at which the exit track would be constructed